Literature

AhlswedeAydinian2009
R. Ahlswede and H. Aydinian: “On error control codes for random network coding” Network Coding, Theory, and Applications, 2009. NetCod'09. Workshop on (2009): 68-73.
https://doi.org/10.1109/NETCOD.2009.5191396
cdc constraints: Ahlswede_Aydinian
mdc constraints: Ahlswede_Aydinian_ilp
AiHonoldLiu2016
Jingmei Ai, Thomas Honold, and Haiteng Liu: “The Expurgation-Augmentation Method for Constructing Good Plane Subspace Codes” arXiv:1601.01502 (2016): 44.
https://arxiv.org/abs/1601.01502
cdc constraints: expurgation_augmentation_general, expurgation_augmentation_special_cases
Andre1954
Johannes André: “Über nicht-Desarguessche Ebenen mit transitiver Translationsgruppe” Mathematische Zeitschrift 60.1 (1954): 156-186.
https://doi.org/10.1007/BF01187370
cdc constraints: spread
AntrobusGluesingLuerssen2018
Jared Antrobus and Heide Gluesing-Luerssen: “Maximal Ferrers Diagram Codes: Constructions and Genericity Considerations” IEEE Transactions on Information Theory 65.10 (2019): 6204-6223.
http://dx.doi.org/10.1109/TIT.2019.2926256
BachocPassuelloVallentin2013
Christine Bachoc, Alberto Passuello, and Frank Vallentin: “Bounds for projective codes from semidefinite programming” Advances of Mathematics in Communications 7.2 (2013): 127-145.
http://dx.doi.org/10.3934/amc.2013.7.127
mdc constraints: semidefinite_programming
BardestaniIranmanesh2015
F. Bardestani and A. Iranmanesh: “Cyclic Orbit Codes with the Normalizer of a Singer Subgroup” Journal of Sciences, Islamic Republic of Iran 26.1 (2015): 49-55.
https://jsciences.ut.ac.ir/article_53218_7187.html
cdc constraints: Bardestani_Iranmanesh
Beutelspacher1975
Albrecht Beutelspacher: “Partial spreads in finite projective spaces and partial designs” Mathematische Zeitschrift 145.3 (1975): 211-229.
https://doi.org/10.1007/BF01215286
cdc constraints: partial_spread_2, spread
BoseBush1952
R. C. Bose and K. A. Bush: “Orthogonal arrays of strength two and three” The Annals of Mathematical Statistics (1952): 508-524.
http://www.jstor.org/stable/2236577
cdc constraints: DrakeFreeman
BosmaCannonPlayoust1997
Wieb Bosma, John Cannon, and Catherine Playoust: “The Magma Algebra System I: The User Language” Journal of Symbolic Computation 24.3-4(1997): 235-265.
https://doi.org/10.1006/jsco.1996.0125
BraunEtzionOstergardVardyWassermann2016
Michael Braun, Tuvi Etzion, Patric Östergård, Alexander Vardy, and Alfred Wassermann: “Existence of q-Analogs of Steiner Systems” Forum of Mathematics, Pi 4 (2016): 14.
http://dx.doi.org/10.1017/fmp.2016.5
cdc codes: \(A_2(13,4;3) \ge 1597245\)
BraunKiermaierNakic2016
Michael Braun, Michael Kiermaier, and Anamari Nakić: “On the automorphism group of a binary q-analog of the Fano plane” European Journal of Combinatorics 51 (2016): 443-457.
https://doi.org/10.1016/j.ejc.2015.07.014
BraunOstergardWassermann2016
Michael Braun, Patric R. J. Östergård, and Alfred Wassermann: “New Lower Bounds for Binary Constant-Dimension Subspace Codes” Experimental Mathematics (2016): 1-5.
http://dx.doi.org/10.1080/10586458.2016.1239145
cdc codes: \(A_2(8,4;3) \ge 1326\), \(A_2(8,4;4) \ge 4801\), \(A_2(9,4;3) \ge 5986\), \(A_2(10,4;3) \ge 23870\), \(A_2(11,4;3) \ge 97526\)
BraunReichelt2014
Michael Braun and Jan Reichelt: “q-Analogs of Packing Designs” Journal of Combinatorial Designs 22.7 (2014): 306-321.
http://dx.doi.org/10.1002/jcd.21376
cdc codes: \(A_2(7,4;3) \ge 329\), \(A_2(8,4;3) \ge 1312\), \(A_2(11,4;3) \ge 92411\), \(A_2(12,4;3) \ge 385515\), \(A_2(14,4;3) \ge 5996178\)
ChenHeWengXu2019
Hao Chen, Xianmang He, Jian Weng, and Liqing Xu: “New Constructions of Subspace Codes Using Subsets of MRD codes in Several Blocks” arXiv:1908.03804 (2019): 22.
https://arxiv.org/abs/1908.03804
cdc constraints: ChenHeWengXu2019_T31, ChenHeWengXu2019_T41, ChenHeWengXu2019_special_Table3
ClimentRequenaSolerEscriva2017
Joan-Josep Climent, Verónica Requena, and Xaro Soler-Escrivà: “A Construction of Orbit Codes” International Castle Meeting on Coding Theory and Applications, ICMCTA 2017: Coding Theory and Applications (2017): 72-83.
https://doi.org/10.1007/978-3-319-66278-7_7
cdc constraints: Orbit_Code_Abeliean_Non_Cyclic
CossidenteKurzMarinoPavese2019
Antonio Cossidente, Sascha Kurz, Giuseppe Marino, and Francesco Pavese: “Combining subspace codes” arXiv:1911.03387.
https://arxiv.org/abs/1911.03387
cdc constraints: CKMP2019_Cor_42, CKMP2019_Cor_45, CKMP2019_Lem_41, CKMP2019_Thm_54, CKMP2019_misc
CossidenteMarinoPavese2019
Antonio Cossidente, Giuseppe Marino, and Francesco Pavese: “Subspace code constructions” arXiv:1905.11021.
https://arxiv.org/abs/1905.11021
cdc constraints: CossidenteMarinoPavese2019_T313, CossidenteMarinoPavese2019_T42_T47
CossidentePavese2016
Antonio Cossidente and Francesco Pavese: “Veronese subspace codes” Designs, Codes and Cryptography 81.3 (2016): 1445–457.
https://doi.org/10.1007/s10623-015-0166-3
cdc constraints: CossidentePavese_n6_d4_k3
CossidentePavese20162
Antonio Cossidente and Francesco Pavese: “On subspace codes” Designs, Codes and Cryptography 78:2 (2016): 527-531.
https://doi.org/10.1007/s10623-014-0018-6
cdc constraints: CossidentePavese162
CossidentePavese2017
Antonio Cossidente and Francesco Pavese: “Subspace Codes in PG(2N-1,Q)” F. Combinatorica 37.6 (2017): 1073–1095.
https://doi.org/10.1007/s00493-016-3354-5
cdc constraints: CossidentePavese14_theorem311, CossidentePavese14_theorem38, CossidentePavese14_theorem43
CossidentePaveseStorme2016
Antonio Cossidente, Francesco Pavese, and Leo Storme: “Optimal subspace codes in PG(4,q)” Advances in Mathematics of Communications 13.3 (2019); 393- 404.
https://arxiv.org/abs/1802.09793
mdc constraints: n5_d3_CPS
mdc codes: \(A_2(5,3) \ge 18\)
CzerwinskiOakden1992
Terry Czerwinski, and David Oakden: “The translation planes of order twenty-five” Journal of Combinatorial Theory, Series A 59.2 (1992): 193-217.
https://doi.org/10.1016/0097-3165(92)90065-3
cdc codes: \(A_5(4,4;2) \ge 26\)
mdc codes: \(A_5(4,4) \ge 26\)
Delsart1973
Philippe Delsart: “An algebraic approach to the association schemes of coding theory” Philips Res. Rep. Suppl. 10 (1973)

cdc constraints: linear_programming_bound
Delsart1978
Philippe Delsart: “Bilinear forms over a finite field, with applications to coding theory” Journal of Combinatorial Theory, Series A 25.3 (1978)
https://doi.org/10.1016/0097-3165(78)90015-8
cdc constraints: linear_programming_bound
Delsart19782
Philippe Delsart: “Hahn Polynomials, Discrete Harmonics, and t-Designs” SIAM Journal on Applied Mathematics 34.1(1978): 157–166.
https://doi.org/10.1137/0134012
cdc constraints: linear_programming_bound
Dembowski1968
Peter Dembowski: “Finite Geometries: Reprint of the 1968 edition” Springer Science & Business Media (2012)
https://doi.org/10.1007/978-3-642-62012-6
cdc constraints: spread
Dempwolff1994
Ulrich Dempwolff: “Translation planes of order 27” Designs, Codes and Cryptography 4.2 (1994): 105-121.
https://doi.org/10.1007/BF01578865
cdc codes: \(A_3(6,6;3) \ge 28\)
mdc codes: \(A_3(6,6) \ge 28\)
DempwolffReifart1983
Ulrich Dempwolff and A. Reifart: “The classification of the translation planes of order 16, I” Geometriae Dedicata 15.2 (1983): 137-153.
https://doi.org/10.1007/BF00147760
cdc codes: \(A_2(8,8;4) \ge 17\)
mdc codes: \(A_2(8,8) \ge 17\)
DrakeFreeman1979
David A. Drake and J. W. Freeman: “Partial t-spreads and group constructible (s,r,μ)-nets” Journal of Geometry 13.2 (1979): 210-216.
https://doi.org/10.1007/BF01919756
cdc constraints: DrakeFreeman
EisfeldStorme2000
J. Eisfeld and L. Storme: “Partial t-spreads and minimal t-covers in finite projective spaces” Intensive Course on Finite Geometry and its Applications Ghent University (2000): 29.
http://www.maths.qmul.ac.uk/~leonard/partialspreads/eisfeldstorme.ps
ElZanatiJordonSeelingerSissokhoSpence2010
S. El-Zanati, H. Jordon, G. Seelinger, P. Sissokho, and L. Spence: “The maximum size of a partial 3-spread in a finite vector space over GF(2)” Designs, Codes and Cryptography 54.2 (2010): 101-107.
https://doi.org/10.1007/s10623-009-9311-1
cdc constraints: partial_spread_1
cdc codes: \(A_2(8,6;3) \ge 34\)
Etzion2013
Tuvi Etzion: “Problems on q-Analogs in Coding Theory.” arXiv:1305.6126 (2013): 37.
http://arxiv.org/abs/1305.6126
mdc codes: \(A_2(6,4) \ge 77\)
Etzion2015
Tuvi Etzion: “A New Approach for Examining q-Steiner Systems” The Electronic Journal of Combinatorics 25.2 (2018): P2.8.
https://arxiv.org/abs/1507.08503
Etzion20152
Tuvi Etzion: “On the Structure of the q-Fano Plane” arXiv:1508.01839 (2015)
https://arxiv.org/abs/1508.01839
EtzionGorlaRavagnaniWachterZeh2016
Tuvi Etzion, Elisa Gorla, Alberto Ravagnani, and Antonia Wachter-Zeh: “Optimal Ferrers Diagram Rank-Metric Codes” IEEE Transactions on Information Theory 62.4 (2016): 1616-1630.
http://doi.org/10.1109/TIT.2016.2522971
cdc constraints: echelon_ferrers, ef_computation, two_pivot_block_construction
mdc constraints: echelon_ferrers, ef_computation
EtzionSilberstein2009
Tuvi Etzion and Natalia Silberstein: “Error-Correcting Codes in Projective Spaces Via Rank-Metric Codes and Ferrers Diagrams” IEEE Transactions on Information Theory 55.7 (2009): 2909-2919.
http://dx.doi.org/10.1109/TIT.2009.2021376
cdc constraints: echelon_ferrers, ef_computation
cdc codes: \(A_2(9,4;4) \ge 36945\), \(A_2(10,4;5) \ge 1167327\), \(A_2(10,6;5) \ge 32841\), \(A_2(12,4;4) \ge 19068061\), \(A_2(13,6;4) \ge 266501\), \(A_3(7,4;3) \ge 6685\), \(A_3(8,4;4) \ge 539578\), \(A_4(7,4;3) \ge 65881\), \(A_4(8,4;4) \ge 16849745\)
mdc constraints: cdc_average_argument, echelon_ferrers, ef_computation
EtzionSilberstein2013
Tuvi Etzion and Natalia Silberstein: “Codes and Designs Related to Lifted MRD Codes” IEEE Transactions on Information Theory 59.2 (2013): 1004-1017.
http://dx.doi.org/10.1109/TIT.2012.2220119
cdc constraints: construction_1, construction_2, construction_3, pending_dots
mdc codes: \(A_2(7,3) \ge 584\)
EtzionStorme2016
Tuvi Etzion and Leo Storme: “Galois geometries and coding theory” Designs, Codes and Cryptography 78.1 (2016): 311–350.
https://doi.org/10.1007/s10623-015-0156-5
EtzionVardy2011
Tuvi Etzion, and Alexander Vardy: “Error-Correcting Codes in Projective Space” IEEE Transactions on Information Theory 57.2 (2011): 1165-1173.
https://doi.org/10.1109/TIT.2010.2095232
cdc constraints: JohnsonLB, JohnsonLB_special, anticode, johnson_1, johnson_2, partial_spread_3, partial_spread_5
cdc codes: \(A_2(9,4;3) \ge 5694\)
mdc constraints: Etzion_Vardy_ilp, gilbert_varshamov
mdc codes: \(A_2(5,3) \ge 18\), \(A_2(6,3) \ge 85\)
EtzionVardy20112
Tuvi Etzion, and Alexander Vardy: “On q-analogs of Steiner systems and covering designs” Advances in Mathematics of Communications 5.2 (2011): 161-176.
https://doi.org/10.3934/amc.2011.5.161
FranklWilson1986
P. Frankl and R. M. Wilson: “The Erdős-Ko-Rado theorem for vector spaces” Journal of Combinatorial Theory, Series A 43.2 (1986): 228–236.
https://doi.org/10.1016/0097-3165(86)90063-4
cdc constraints: anticode
GAP
The GAP Group, “GAP -- Groups, Algorithms, and Programming,” Version 4.8.10 (2018)
https://www.gap-system.org
Gabidulin1985
È. M. Gabidulin: “Theory of Codes with Maximum Rank Distance” Problemy Peredachi Informatsii 21.1 (1985): 3-16.
http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=ppi&paperid=967&option_lang=eng
cdc constraints: LMRD
cdc codes: \(A_2(4,4;2) \ge 4\), \(A_2(5,4;2) \ge 8\), \(A_2(6,4;2) \ge 16\), \(A_2(6,4;3) \ge 64\), \(A_2(6,6;3) \ge 8\), \(A_2(7,4;2) \ge 32\), \(A_2(7,4;3) \ge 256\), \(A_2(7,6;3) \ge 16\), \(A_2(8,4;2) \ge 64\), \(A_2(8,4;3) \ge 1024\), \(A_2(8,4;4) \ge 4096\), \(A_2(8,6;3) \ge 32\), \(A_2(8,6;4) \ge 256\), \(A_2(8,8;4) \ge 16\), \(A_2(9,4;2) \ge 128\), \(A_2(9,4;3) \ge 4096\), \(A_2(9,6;3) \ge 64\), \(A_2(9,6;4) \ge 1024\), \(A_2(9,8;4) \ge 32\), \(A_2(10,4;2) \ge 256\), \(A_2(10,6;3) \ge 128\), \(A_2(10,6;4) \ge 4096\), \(A_2(10,8;4) \ge 64\), \(A_2(10,8;5) \ge 1024\), \(A_2(10,10;5) \ge 32\), \(A_2(11,4;2) \ge 512\), \(A_2(11,6;3) \ge 256\), \(A_2(11,6;4) \ge 16384\), \(A_2(11,8;4) \ge 128\), \(A_2(11,8;5) \ge 4096\), \(A_2(11,10;5) \ge 64\), \(A_2(12,4;2) \ge 1024\), \(A_2(12,6;3) \ge 512\), \(A_2(12,8;4) \ge 256\), \(A_2(12,10;5) \ge 128\), \(A_2(12,10;6) \ge 4096\), \(A_2(12,12;6) \ge 64\), \(A_2(13,4;2) \ge 2048\), \(A_2(13,6;3) \ge 1024\), \(A_2(13,8;4) \ge 512\), \(A_2(13,10;5) \ge 256\), \(A_2(13,12;6) \ge 128\), \(A_2(14,4;2) \ge 4096\), \(A_2(14,6;3) \ge 2048\), \(A_2(14,8;4) \ge 1024\), \(A_2(14,10;5) \ge 512\), \(A_2(14,12;6) \ge 256\), \(A_2(14,14;7) \ge 128\), \(A_2(15,4;2) \ge 8192\), \(A_2(15,6;3) \ge 4096\), \(A_2(15,8;4) \ge 1048\), \(A_2(15,10;5) \ge 1024\), \(A_2(15,12;6) \ge 512\), \(A_2(15,14;7) \ge 256\), \(A_2(16,6;3) \ge 8192\), \(A_2(16,8;4) \ge 4096\), \(A_2(16,10;5) \ge 1048\), \(A_2(16,12;6) \ge 1024\), \(A_2(16,14;7) \ge 512\), \(A_2(16,16;8) \ge 256\), \(A_2(17,8;4) \ge 8192\), \(A_2(17,10;5) \ge 4096\), \(A_2(17,12;6) \ge 1048\), \(A_2(17,14;7) \ge 1024\), \(A_2(17,16;8) \ge 512\), \(A_2(18,10;5) \ge 8192\), \(A_2(18,12;6) \ge 4096\), \(A_2(18,14;7) \ge 1048\), \(A_2(18,16;8) \ge 1024\), \(A_2(18,18;9) \ge 512\), \(A_2(19,12;6) \ge 8192\), \(A_2(19,14;7) \ge 4096\), \(A_2(19,16;8) \ge 1048\), \(A_2(19,18;9) \ge 1024\), \(A_3(4,4;2) \ge 9\), \(A_3(5,4;2) \ge 27\), \(A_3(6,4;2) \ge 81\), \(A_3(6,4;3) \ge 729\), \(A_3(6,6;3) \ge 27\), \(A_3(7,4;2) \ge 243\), \(A_3(7,4;3) \ge 6561\), \(A_3(7,6;3) \ge 81\), \(A_3(8,4;2) \ge 729\), \(A_3(8,6;3) \ge 243\), \(A_3(8,6;4) \ge 6561\), \(A_3(8,8;4) \ge 81\), \(A_3(9,4;2) \ge 2187\), \(A_3(9,6;3) \ge 729\), \(A_3(9,8;4) \ge 243\), \(A_3(10,4;2) \ge 6561\), \(A_3(10,6;3) \ge 2187\), \(A_3(10,8;4) \ge 729\), \(A_3(10,10;5) \ge 243\), \(A_3(11,6;3) \ge 6561\), \(A_3(11,8;4) \ge 2187\), \(A_3(11,10;5) \ge 729\), \(A_3(12,8;4) \ge 6561\), \(A_3(12,10;5) \ge 2187\), \(A_3(12,12;6) \ge 729\), \(A_3(13,10;5) \ge 6561\), \(A_3(13,12;6) \ge 2187\), \(A_3(14,12;6) \ge 6561\), \(A_3(14,14;7) \ge 2187\), \(A_3(15,14;7) \ge 6561\), \(A_3(16,16;8) \ge 6561\), \(A_5(4,4;2) \ge 25\), \(A_5(5,4;2) \ge 125\), \(A_5(6,4;2) \ge 625\), \(A_5(6,6;3) \ge 125\), \(A_5(7,4;2) \ge 3125\), \(A_5(7,6;3) \ge 625\), \(A_5(8,6;3) \ge 3125\), \(A_5(8,8;4) \ge 625\), \(A_5(9,8;4) \ge 3125\), \(A_5(10,10;5) \ge 3125\), \(A_7(4,4;2) \ge 49\), \(A_7(5,4;2) \ge 343\), \(A_7(6,4;2) \ge 2401\), \(A_7(6,6;3) \ge 343\), \(A_7(7,6;3) \ge 2401\), \(A_7(8,8;4) \ge 2401\)
mdc codes: \(A_2(4,4) \ge 4\), \(A_2(5,4) \ge 9\), \(A_2(6,4) \ge 16\), \(A_2(6,4) \ge 64\), \(A_2(6,6) \ge 8\), \(A_2(7,4) \ge 32\), \(A_2(7,4) \ge 256\), \(A_2(7,6) \ge 16\), \(A_2(8,4) \ge 64\), \(A_2(8,4) \ge 1024\), \(A_2(8,4) \ge 4096\), \(A_2(8,6) \ge 32\), \(A_2(8,6) \ge 256\), \(A_2(8,8) \ge 16\), \(A_2(9,4) \ge 128\), \(A_2(9,4) \ge 4096\), \(A_2(9,6) \ge 64\), \(A_2(9,6) \ge 1024\), \(A_2(9,8) \ge 32\), \(A_2(10,4) \ge 256\), \(A_2(10,6) \ge 128\), \(A_2(10,6) \ge 4096\), \(A_2(10,8) \ge 64\), \(A_2(10,8) \ge 1024\), \(A_2(10,10) \ge 32\), \(A_2(11,4) \ge 512\), \(A_2(11,6) \ge 256\), \(A_2(11,6) \ge 16384\), \(A_2(11,8) \ge 128\), \(A_2(11,8) \ge 4096\), \(A_2(11,10) \ge 64\), \(A_2(12,4) \ge 1024\), \(A_2(12,6) \ge 512\), \(A_2(12,8) \ge 256\), \(A_2(12,10) \ge 128\), \(A_2(12,10) \ge 4096\), \(A_2(12,12) \ge 64\), \(A_2(13,4) \ge 2048\), \(A_2(13,6) \ge 1024\), \(A_2(13,8) \ge 512\), \(A_2(13,10) \ge 256\), \(A_2(13,12) \ge 128\), \(A_2(14,4) \ge 4096\), \(A_2(14,6) \ge 2048\), \(A_2(14,8) \ge 1024\), \(A_2(14,10) \ge 512\), \(A_2(14,12) \ge 256\), \(A_2(14,14) \ge 128\), \(A_2(15,4) \ge 8192\), \(A_2(15,6) \ge 4096\), \(A_2(15,8) \ge 1048\), \(A_2(15,10) \ge 1024\), \(A_2(15,12) \ge 512\), \(A_2(15,14) \ge 256\), \(A_2(16,6) \ge 8192\), \(A_2(16,8) \ge 4096\), \(A_2(16,10) \ge 1048\), \(A_2(16,12) \ge 1024\), \(A_2(16,14) \ge 512\), \(A_2(16,16) \ge 256\), \(A_2(17,8) \ge 8192\), \(A_2(17,10) \ge 4096\), \(A_2(17,12) \ge 1048\), \(A_2(17,14) \ge 1024\), \(A_2(17,16) \ge 512\), \(A_2(18,10) \ge 8192\), \(A_2(18,12) \ge 4096\), \(A_2(18,14) \ge 1048\), \(A_2(18,16) \ge 1024\), \(A_2(18,18) \ge 512\), \(A_2(19,12) \ge 8192\), \(A_2(19,14) \ge 4096\), \(A_2(19,16) \ge 1048\), \(A_2(19,18) \ge 1024\), \(A_3(4,4) \ge 9\), \(A_3(5,4) \ge 27\), \(A_3(6,4) \ge 81\), \(A_3(6,4) \ge 729\), \(A_3(6,6) \ge 27\), \(A_3(7,4) \ge 243\), \(A_3(7,4) \ge 6561\), \(A_3(7,6) \ge 81\), \(A_3(8,4) \ge 729\), \(A_3(8,6) \ge 243\), \(A_3(8,6) \ge 6561\), \(A_3(8,8) \ge 81\), \(A_3(9,4) \ge 2187\), \(A_3(9,6) \ge 729\), \(A_3(9,8) \ge 243\), \(A_3(10,4) \ge 6561\), \(A_3(10,6) \ge 2187\), \(A_3(10,8) \ge 729\), \(A_3(10,10) \ge 243\), \(A_3(11,6) \ge 6561\), \(A_3(11,8) \ge 2187\), \(A_3(11,10) \ge 729\), \(A_3(12,8) \ge 6561\), \(A_3(12,10) \ge 2187\), \(A_3(12,12) \ge 729\), \(A_3(13,10) \ge 6561\), \(A_3(13,12) \ge 2187\), \(A_3(14,12) \ge 6561\), \(A_3(14,14) \ge 2187\), \(A_3(15,14) \ge 6561\), \(A_3(16,16) \ge 6561\), \(A_5(4,4) \ge 25\), \(A_5(5,4) \ge 125\), \(A_5(6,4) \ge 625\), \(A_5(6,6) \ge 125\), \(A_5(7,4) \ge 3125\), \(A_5(7,6) \ge 625\), \(A_5(8,6) \ge 3125\), \(A_5(8,8) \ge 625\), \(A_5(9,8) \ge 3125\), \(A_5(10,10) \ge 3125\), \(A_7(4,4) \ge 49\), \(A_7(5,4) \ge 343\), \(A_7(6,4) \ge 2401\), \(A_7(6,6) \ge 343\), \(A_7(7,6) \ge 2401\), \(A_7(8,8) \ge 2401\)
GluesingLuerssenTroha2016
Heide Gluesing-Luerssen and Carolyn Troha: “Construction of subspace codes through linkage” Advances in Mathematics of Communications 10.3 (2016): 525-540.
https://doi.org/10.3934/amc.2016023
cdc constraints: linkage_GLT
GordonShawSoicher2000
Neil A. Gordon, Ron Shaw, and Leonard H. Soicher: “Classification of partial spreads in PG(4, 2)” Mathematics Research Reports (University of Hull) XIII (2000) No.1.
http://www.maths.qmul.ac.uk/~lsoicher/PG42partialspreads.ps
cdc codes: \(A_2(5,4;2) \ge 9\)
GorlaRavagnani2017
Elisa Gorla and Alberto Ravagnani: “Subspace Codes from Ferrers Diagrams” Journal of Algebra and Its Applications 16.7 (2017).
https://doi.org/10.1142/S0219498817501316
cdc constraints: Gorla_Ravagnani_2014, echelon_ferrers, ef_computation, pending_dots
mdc constraints: echelon_ferrers, ef_computation
GutierrezMolina2015
Ismael Gutierrez and Ivan Molina: “Some constructions of cyclic and quasi-cyclic subspaces codes” arXiv:1504.04553 (2015) 14.
http://arxiv.org/abs/1504.04553
cdc codes: \(A_2(8,4;4) \ge 2992\), \(A_2(10,4;3) \ge 21483\), \(A_2(10,10;5) \ge 33\)
GutierrezMolina2020
Ismael Gutiérrez-García and Ivan Molina Naizir: “Finding cliques in Projective Space: A method for construction of cyclic Grassmannian codes” IEEE Access 8 (2020): 51333-51339.
https://ieeexplore.ieee.org/abstract/document/9035454
cdc codes: \(A_2(6,4;3) \ge 63\), \(A_2(7,4;3) \ge 254\), \(A_2(8,4;3) \ge 1275\), \(A_2(8,4;4) \ge 4420\), \(A_2(8,4;4) \ge 4590\), \(A_2(9,4;3) \ge 5621\)
HallSwiftWalker1956
Marshall Hall, Jr., J. Dean Swift and Robert J. Walker: “Uniqueness of the Projective Plane of Order Eight” Mathematical Tables and Other Aids to Computation 10.56 (1992): 186-194.
http://doi.org/10.2307/2001913
cdc codes: \(A_2(6,6;3) \ge 9\)
mdc codes: \(A_2(6,6) \ge 9\)
He2019
Xianmang He: “A Hierarchical-based Greedy Algorithm for Echelon-Ferrers Construction” arXiv:1911.00508 (2019): 18.
https://arxiv.org/abs/1911.00508
cdc constraints: EF_special
Heinlein2018
Daniel Heinlein: “New LMRD bounds for constant dimension codes and improved constructions” IEEE Transactions on Information Theory 65.8 (2019): 4822-4830.
https://arxiv.org/abs/1801.04803
cdc codes: \(A_2(10,6;5) \ge 32923\), \(A_2(11,6;4) \ge 16717\), \(A_2(11,6;5) \ge 263478\), \(A_2(12,6;4) \ge 66839\), \(A_2(12,6;5) \ge 2105077\), \(A_2(13,6;4) \ge 267897\)
Heinlein2019
Daniel Heinlein: “Generalized linkage construction for constant-dimension codes” arXiv:1910.11195 (2019): 17.
https://arxiv.org/abs/1910.11195
cdc constraints: generalized_linkage, generalized_linkage_multipleblocks
HeinleinHonoldKiermaierKurzWassermann2017
Daniel Heinlein, Thomas Honold, Michael Kiermaier, Sascha Kurz, and Alfred Wassermann: “Classifying optimal binary subspace codes of length 8, constant dimension 4 and minimum distance 6” Designs, Codes and Cryptography 87.2-3 (2019): 375-391.
https://doi.org/10.1007/s10623-018-0544-8
cdc constraints: HKK_theorem_3_3_i_lower_bound_cdc, HKK_theorem_3_3_i_upper_bound_cdc
cdc codes: \(A_2(8,6;4) \ge 257\)
mdc constraints: HKK_theorem_3_3_i_lower_bound_mdc, HKK_theorem_3_3_i_upper_bound_mdc
mdc codes: \(A_2(8,6) \ge 257\)
HeinleinIhringer2018
Daniel Heinlein, Ferdinand Ihringer: “New and Updated Semidefinite Programming Bounds for Subspace Codes” Advances in Mathematics of Communications (to appear): 21.
http://doi.org/10.3934/amc.2020034
mdc constraints: heinlein_ihringer_semidefinite_programming
HeinleinKiermaierKurzWassermann2017
Daniel Heinlein, Michael Kiermaier, Sascha Kurz, and Alfred Wassermann: “A subspace code of size 333 in the setting of a binary q-analog of the Fano plane” Advances in Mathematics of Communications 13.3 (2019): 457-475.
https://arxiv.org/abs/1708.06224
cdc codes: \(A_2(7,4;3) \ge 333\)
HeinleinKurz2017
Daniel Heinlein and Sascha Kurz: “A new upper bound for subspace codes” arXiv:1703.08712 (2017): 9.
https://arxiv.org/abs/1703.08712
cdc constraints: special_case_2_8_6_4
mdc codes: \(A_2(7,5) \ge 33\)
HeinleinKurz20172
Daniel Heinlein and Sascha Kurz: “Asymptotic bounds for the sizes of constant dimension codes and an improved lower bound” Coding Theory and Applications. ICMCTA 2017. Lecture Notes in Computer Science. vol 10495. (2017): 163-191.
https://doi.org/10.1007/978-3-319-66278-7_15
cdc constraints: Ahlswede_Aydinian
HeinleinKurz20173
Daniel Heinlein and Sascha Kurz: “Coset Construction for Subspace Codes” IEEE Transactions on Information Theory 63.12 (2017) 7651 - 7660.
https://doi.org/10.1109/TIT.2017.2753822
cdc constraints: coset_construction, coset_construction_parallelism_part
cdc codes: \(A_2(9,6;4) \ge 1033\), \(A_2(10,6;4) \ge 4173\)
HeinleinKurz2018
Daniel Heinlein and Sascha Kurz: “Binary Subspace Codes in Small Ambient Spaces” Advances in Mathematics of Communications 12.4 (2018): 817-839.
https://doi.org/10.3934/amc.2018048
mdc constraints: special_cases_upper_notderived_2
mdc codes: \(A_2(6,3) \ge 108\), \(A_2(8,6) \ge 257\), \(A_2(8,7) \ge 17\)
Hirschfeld1998
J. W. P. Hirschfeld: “Projective geometries over finite fields” The Clarendon Press Oxford University Press New York, second edition (1998).

HoKoetterMedardKargerEffros
Tracey Ho, Ralf Koetter, Muriel Medard, David R. Karger, and Michelle Effros: “The Benefits of Coding over Routing in a Randomized Setting” (2003)
https://authors.library.caltech.edu/7381/1/HOTisit03a.pdf
HonoldKiermaier2016
Thomas Honold and Michael Kiermaier: “On putative q-Analogues of the Fano Plane and Related Combinatorial Structures” Dynamical Systems, Number Theory and Applications (2016): 141-175.
https://doi.org/10.1142/9789814699877_0008
cdc constraints: construction_HK15
cdc codes: \(A_2(7,4;3) \ge 329\), \(A_3(7,4;3) \ge 6977\)
HonoldKiermaierKurz2015
Thomas Honold, Michael Kiermaier, and Sascha Kurz: “Optimal binary subspace codes of length 6, constant dimension 3 and minimum subspace distance 4” Topics in Finite Fields 632 (2015): 157-176.
http://dx.doi.org/10.1090/conm/632
cdc constraints: HonoldKiermaierKurz_n6_d4_k3
cdc codes: \(A_2(6,4;3) \ge 77\)
HonoldKiermaierKurz2016
Thomas Honold, Michael Kiermaier, and Sascha Kurz: “Classification of large partial plane spreads in PG(6, 2) and related combinatorial objects” Journal of Geometry 110 (2018): paper number 5.
https://arxiv.org/abs/1606.07655
cdc codes: \(A_2(7,6;3) \ge 17\)
mdc codes: \(A_2(7,5) \ge 34\)
HonoldKiermaierKurz20162
Thomas Honold, Michael Kiermaier, and Sascha Kurz: “Partial spreads and vector space partitions” arXiv:1611.06328 (2018) pages 131-170 in Network Coding and Subspace Designs, Eds. M. Greferath, M.O. Pavčević, N. Silberstein, and A. Vazquez-Castro, Springer
https://arxiv.org/abs/1611.06328
cdc constraints: partial_spread_HKK16_T10
cdc codes: \(A_2(8,6;3) \ge 34\)
HonoldKiermaierKurz20163
Thomas Honold, Michael Kiermaier, and Sascha Kurz: “Constructions and Bounds for Mixed-Dimension Subspace Codes” Advances in Mathematics of Communications 10.3 (2016): 649-682.
http://dx.doi.org/10.3934/amc.2016033
cdc constraints: HKK_lemma_2_4_lower_bound, HKK_lemma_2_4_upper_bound, HKK_theorem_3_1_ii_cdc, HKK_theorem_3_2_ii_cdc, HKK_theorem_3_3_i_lower_bound_cdc, HKK_theorem_3_3_i_upper_bound_cdc
cdc codes: \(A_2(4,4;2) \ge 5\), \(A_2(6,6;3) \ge 9\), \(A_2(7,6;3) \ge 17\), \(A_2(8,8;4) \ge 17\), \(A_3(4,4;2) \ge 10\), \(A_3(6,6;3) \ge 28\), \(A_4(4,4;2) \ge 17\), \(A_5(4,4;2) \ge 26\), \(A_7(4,4;2) \ge 50\)
mdc constraints: HKK_theorem_3_1_i, HKK_theorem_3_3_i_lower_bound_A_q_6_4, HKK_theorem_3_3_i_lower_bound_mdc, HKK_theorem_3_3_i_upper_bound_A_q_6_4, HKK_theorem_3_3_i_upper_bound_mdc, d2, improved_cdc_lower_bound, improved_cdc_upper_bound, layer_construction, neqdeven, neven_deqnm1, nodd_deqnm1, nodd_deqnm2_e, nodd_deqnm2_l, nodd_deqnm2_u, special_cases_upper_notderived
mdc codes: \(A_2(2,2) \ge 3\), \(A_2(3,2) \ge 8\), \(A_2(4,2) \ge 37\), \(A_2(5,2) \ge 187\), \(A_2(6,2) \ge 1521\), \(A_2(7,2) \ge 14606\), \(A_2(8,2) \ge 222379\), \(A_2(9,2) \ge 4141729\), \(A_2(10,2) \ge 121919127\), \(A_2(11,2) \ge 4466744372\), \(A_2(12,2) \ge 258501941713\), \(A_2(13,2) \ge 18779494904263\), \(A_2(14,2) \ge 2154948394379709\), \(A_2(15,2) \ge 311738238353418074\), \(A_2(16,2) \ge 71234670515346760951\), \(A_2(17,2) \ge 20564497734374127115501\), \(A_2(18,2) \ge 9377928494585763558839523\), \(A_2(19,2) \ge 5408580882753786431279731328\), \(A_3(2,2) \ge 4\), \(A_3(3,2) \ge 14\), \(A_3(4,2) \ge 132\), \(A_3(5,2) \ge 1332\), \(A_3(6,2) \ge 34608\), \(A_3(7,2) \ge 1026328\), \(A_3(8,2) \ge 77705744\), \(A_3(9,2) \ge 6860614544\), \(A_3(10,2) \ge 1543125682496\), \(A_3(11,2) \ge 407650394221536\), \(A_3(12,2) \ge 274173842939879488\), \(A_3(13,2) \ge 217094161964411629888\), \(A_3(14,2) \ge 437555577947523368326912\), \(A_3(15,2) \ge 1039076627439939472446430592\), \(A_3(16,2) \ge 6280522010999565623871130419456\), \(A_3(17,2) \ge 44739207544278383273349960118169856\), \(A_3(18,2) \ge 811157108360138243362895549411912131584\), \(A_3(19,2) \ge 17334224582198669278770650291735912677010944\), \(A_4(2,2) \ge 5\), \(A_4(3,2) \ge 22\), \(A_4(4,2) \ge 359\), \(A_4(5,2) \ge 6139\), \(A_4(6,2) \ge 379535\), \(A_4(7,2) \ge 25704928\), \(A_4(8,2) \ge 6269331761\), \(A_4(9,2) \ge 1693943516101\), \(A_4(10,2) \ge 1646849322856025\), \(A_4(11,2) \ge 1778690155851898282\), \(A_4(12,2) \ge 6910942435714698022139\), \(A_4(13,2) \ge 29851806244777155815534479\), \(A_4(14,2) \ge 463845192731753530965728186915\), \(A_4(15,2) \ge 8013977155310915080016613977522548\), \(A_4(16,2) \ge 498066010787890008155987967168551891141\), \(A_4(17,2) \ge 34420514954543599371235443603262517261964121\), \(A_4(18,2) \ge 8556777750864526187911418804965026926384160536045\), \(A_4(19,2) \ge 2365372578679512182314915604695550782642685560327742782\), \(A_5(2,2) \ge 6\), \(A_5(3,2) \ge 32\), \(A_5(4,2) \ge 808\), \(A_5(5,2) \ge 21088\), \(A_5(6,2) \ge 2566368\), \(A_5(7,2) \ge 333062144\), \(A_5(8,2) \ge 201161057920\), \(A_5(9,2) \ge 130383335603200\), \(A_5(10,2) \ge 393153256760148480\), \(A_5(11,2) \ge 1273824505480738144256\), \(A_5(12,2) \ge 19199483621099329716140032\), \(A_5(13,2) \ge 311019164051283235528140685312\), \(A_5(14,2) \ge 23437491673790886665269226565230592\), \(A_5(15,2) \ge 1898343109664891700541791141575543226368\), \(A_5(16,2) \ge 715259279871732236829984542779763924521222144\), \(A_5(17,2) \ge 289665171234910201562211053424258500847622945767424\), \(A_5(18,2) \ge 545700103157547923454032782855873119865046931321370312704\), \(A_5(19,2) \ge 1104985699940665958989412433957199720026143707690553670348308480\), \(A_7(2,2) \ge 8\), \(A_7(3,2) \ge 58\), \(A_7(4,2) \ge 2852\), \(A_7(5,2) \ge 142852\), \(A_7(6,2) \ge 48216416\), \(A_7(7,2) \ge 16868199016\), \(A_7(8,2) \ge 39741980063504\), \(A_7(9,2) \ge 97292877050623504\), \(A_7(10,2) \ge 1603926790896596642432\), \(A_7(11,2) \ge 27484891360591082207177632\), \(A_7(12,2) \ge 3171542305632803880032619871808\), \(A_7(13,2) \ge 380430351919414427641088029723551808\), \(A_7(14,2) \ge 307288356314229806376292964555107145137664\), \(A_7(15,2) \ge 258017037295312889339178547120512162294536808064\), \(A_7(16,2) \ge 1458870888924854760006394404592890205261685632368271616\), \(A_7(17,2) \ge 8574664161553264151428650758674596275586758673726248708751616\), \(A_7(18,2) \ge 339377901880889399149257884684947716532422547051645404793668374448128\), \(A_7(19,2) \ge 13963100154451053905283995421210739233865967405270492184173660353525630908928\), \(A_8(2,2) \ge 9\), \(A_8(3,2) \ge 74\), \(A_8(4,2) \ge 4747\), \(A_8(5,2) \ge 308947\), \(A_8(6,2) \ge 156162843\), \(A_8(7,2) \ge 81183411548\), \(A_8(8,2) \ge 327659429183389\), \(A_8(9,2) \ge 1362441066883081189\), \(A_8(10,2) \ge 43980428697245703899181\), \(A_8(11,2) \ge 1462964924763536311525587566\), \(A_8(12,2) \ge 377791931723329465422341499645103\), \(A_8(13,2) \ge 100534656304920922914050539639639904503\), \(A_8(14,2) \ge 207693511973813534610553803431729000698754367\), \(A_8(15,2) \ge 442156353998327362270757228269337175350417971210112\), \(A_8(16,2) \ge 7307566690035440019173154780461391215091503147059515595201\), \(A_8(17,2) \ge 124455958577714097108024810199576169356215499446391670599398702601\), \(A_8(18,2) \ge 16455177560026238105621735732130983984862055222836334866940628579275104849\), \(A_8(19,2) \ge 2241999255265488707954469269918612450261829794217662835681983673768665755238765714\), \(A_9(2,2) \ge 10\), \(A_9(3,2) \ge 92\), \(A_9(4,2) \ge 7464\), \(A_9(5,2) \ge 612624\), \(A_9(6,2) \ge 441959520\), \(A_9(7,2) \ge 326112922048\), \(A_9(8,2) \ge 2114530467299456\), \(A_9(9,2) \ge 14040675863296123136\), \(A_9(10,2) \ge 819240506883749877900800\), \(A_9(11,2) \ge 48957810801345386907074092032\), \(A_9(12,2) \ge 25708733095428691935741540859070464\), \(A_9(13,2) \ge 13827163231734033747834068233653363871744\), \(A_9(14,2) \ge 65348177799201782965568701172796668994207047680\), \(A_9(15,2) \ge 316321223358800850063408234086378980344607376256647168\), \(A_9(16,2) \ge 13454610940042444841139807389178448386407410305391634922110976\), \(A_9(17,2) \ge 586149629489783561417254875882304339104815581674314737015897299419136\), \(A_9(18,2) \ge 224384992517708719472523093298570420971408321696723352971792224732784491888640\), \(A_9(19,2) \ge 87977915141973353972841022973087980756687157787143031068804885978790883149243634941952\), \(A_2(4,3) \ge 5\), \(A_2(4,4) \ge 5\), \(A_2(5,3) \ge 18\), \(A_2(6,3) \ge 104\), \(A_2(6,4) \ge 77\), \(A_2(6,5) \ge 9\), \(A_2(6,6) \ge 9\), \(A_2(7,3) \ge 593\), \(A_2(7,5) \ge 34\), \(A_2(7,6) \ge 17\), \(A_2(8,6) \ge 257\), \(A_2(8,8) \ge 17\), \(A_3(4,4) \ge 10\), \(A_3(6,6) \ge 28\), \(A_4(4,4) \ge 17\), \(A_5(4,4) \ge 26\), \(A_7(4,4) \ge 50\), \(A_2(3,3) \ge 2\), \(A_2(5,5) \ge 2\), \(A_2(7,7) \ge 2\), \(A_2(9,9) \ge 2\), \(A_2(11,11) \ge 2\), \(A_2(13,13) \ge 2\), \(A_2(15,15) \ge 2\), \(A_2(17,17) \ge 2\), \(A_2(19,19) \ge 2\), \(A_3(3,3) \ge 2\), \(A_3(5,5) \ge 2\), \(A_3(7,7) \ge 2\), \(A_3(9,9) \ge 2\), \(A_3(11,11) \ge 2\), \(A_3(13,13) \ge 2\), \(A_3(15,15) \ge 2\), \(A_3(17,17) \ge 2\), \(A_3(19,19) \ge 2\), \(A_4(3,3) \ge 2\), \(A_4(5,5) \ge 2\), \(A_4(7,7) \ge 2\), \(A_4(9,9) \ge 2\), \(A_4(11,11) \ge 2\), \(A_4(13,13) \ge 2\), \(A_4(15,15) \ge 2\), \(A_4(17,17) \ge 2\), \(A_4(19,19) \ge 2\), \(A_5(3,3) \ge 2\), \(A_5(5,5) \ge 2\), \(A_5(7,7) \ge 2\), \(A_5(9,9) \ge 2\), \(A_5(11,11) \ge 2\), \(A_5(13,13) \ge 2\), \(A_5(15,15) \ge 2\), \(A_5(17,17) \ge 2\), \(A_5(19,19) \ge 2\), \(A_7(3,3) \ge 2\), \(A_7(5,5) \ge 2\), \(A_7(7,7) \ge 2\), \(A_7(9,9) \ge 2\), \(A_7(11,11) \ge 2\), \(A_7(13,13) \ge 2\), \(A_7(15,15) \ge 2\), \(A_7(17,17) \ge 2\), \(A_7(19,19) \ge 2\), \(A_8(3,3) \ge 2\), \(A_8(5,5) \ge 2\), \(A_8(7,7) \ge 2\), \(A_8(9,9) \ge 2\), \(A_8(11,11) \ge 2\), \(A_8(13,13) \ge 2\), \(A_8(15,15) \ge 2\), \(A_8(17,17) \ge 2\), \(A_8(19,19) \ge 2\), \(A_9(3,3) \ge 2\), \(A_9(5,5) \ge 2\), \(A_9(7,7) \ge 2\), \(A_9(9,9) \ge 2\), \(A_9(11,11) \ge 2\), \(A_9(13,13) \ge 2\), \(A_9(15,15) \ge 2\), \(A_9(17,17) \ge 2\), \(A_9(19,19) \ge 2\)
HonoldKiermaierKurz2018
Thomas Honold, Michael Kiermaier, and Sascha Kurz: “Johnson type bounds for mixed dimension subspace codes” The Electronic Journal of Combinatorics 26.3 (2019): 21.
https://arxiv.org/abs/1808.03580
mdc constraints: johnson_MDC_Lemma_2, johnson_MDC_Lemma_3, johnson_MDC_Lemma_4, johnson_MDC_Lemma_5, johnson_MDC_Lemma_6, johnson_MDC_Proposition_5, special_improved_cdc_upper_bound
HorlemannTrautmannManganielloBraunRosenthal2017
Anna-Lena Horlemann-Trautmann, Felice Manganiello, Michael Braun, and Joachim Rosenthal: “Correction to cyclic orbit codes” IEEE Transactions on Information Theory 63.11 (2017): 7616-7616.
https://doi.org/10.1109/TIT.2017.2717855
HorlemannTrautmannRosenthal2018
Anna-Lena Horlemann-Trautmann and Joachim Rosenthal: “Constructions of constant dimension codes” In Network Coding and Subspace Designs Springer (2018): 25-42.
https://doi.org/10.1007/978-3-319-70293-3_2
IhringerSinXiang2017
Ferdinand Ihringer, Peter Sin, and Qing Xiang: “New Bounds for Partial Spreads of \(H(2d - 1, q^2)\) and Partial Ovoids of the Ree-Tits Octagon” arXiv:1604.06172 (2017)
https://arxiv.org/abs/1604.06172
cdc constraints: prank
KhaleghiSilvaKschischang2009
Azadeh Khaleghi, Danilo Silva, and Frank R. Kschischang: “Subspace Codes” Cryptography and Coding. IMACC 2009. Lecture Notes in Computer Science, vol 5921. (2009): 1-21.
https://doi.org/10.1007/978-3-642-10868-6_1
mdc constraints: Ahlswede_Aydinian_ilp
KiermaierKurz2017
Michael Kiermaier and Sascha Kurz: “An improvement of the Johnson bound for subspace codes” arXiv:1707.00650
https://arxiv.org/abs/1707.00650
cdc constraints: improved_johnson
KiermaierKurzWassermann2018
Michael Kiermaier, Sascha Kurz, and Alfred Wassermann: “The order of the automorphism group of a binary q-analog of the Fano plane is at most two” Designs, Codes and Cryptography 86.2 (2018): 239-250.
https://doi.org/10.1007/s10623-017-0360-6
KoetterKschischang2008
Ralf Koetter and Frank R. Kschischang: “Coding for Errors and Erasures in Random Network Coding” IEEE Transactions on Information Theory 54.8 (2008): 3579-3591.
http://dx.doi.org/10.1109/TIT.2008.926449
cdc constraints: LMRD, singleton, sphere_covering, sphere_packing
cdc codes: \(A_2(4,4;2) \ge 4\), \(A_2(5,4;2) \ge 8\), \(A_2(6,4;2) \ge 16\), \(A_2(6,4;3) \ge 64\), \(A_2(6,6;3) \ge 8\), \(A_2(7,4;2) \ge 32\), \(A_2(7,4;3) \ge 256\), \(A_2(7,6;3) \ge 16\), \(A_2(8,4;2) \ge 64\), \(A_2(8,4;3) \ge 1024\), \(A_2(8,4;4) \ge 4096\), \(A_2(8,6;3) \ge 32\), \(A_2(8,6;4) \ge 256\), \(A_2(8,8;4) \ge 16\), \(A_2(9,4;2) \ge 128\), \(A_2(9,4;3) \ge 4096\), \(A_2(9,6;3) \ge 64\), \(A_2(9,6;4) \ge 1024\), \(A_2(9,8;4) \ge 32\), \(A_2(10,4;2) \ge 256\), \(A_2(10,6;3) \ge 128\), \(A_2(10,6;4) \ge 4096\), \(A_2(10,8;4) \ge 64\), \(A_2(10,8;5) \ge 1024\), \(A_2(10,10;5) \ge 32\), \(A_2(11,4;2) \ge 512\), \(A_2(11,6;3) \ge 256\), \(A_2(11,6;4) \ge 16384\), \(A_2(11,8;4) \ge 128\), \(A_2(11,8;5) \ge 4096\), \(A_2(11,10;5) \ge 64\), \(A_2(12,4;2) \ge 1024\), \(A_2(12,6;3) \ge 512\), \(A_2(12,8;4) \ge 256\), \(A_2(12,10;5) \ge 128\), \(A_2(12,10;6) \ge 4096\), \(A_2(12,12;6) \ge 64\), \(A_2(13,4;2) \ge 2048\), \(A_2(13,6;3) \ge 1024\), \(A_2(13,8;4) \ge 512\), \(A_2(13,10;5) \ge 256\), \(A_2(13,12;6) \ge 128\), \(A_2(14,4;2) \ge 4096\), \(A_2(14,6;3) \ge 2048\), \(A_2(14,8;4) \ge 1024\), \(A_2(14,10;5) \ge 512\), \(A_2(14,12;6) \ge 256\), \(A_2(14,14;7) \ge 128\), \(A_2(15,4;2) \ge 8192\), \(A_2(15,6;3) \ge 4096\), \(A_2(15,8;4) \ge 1048\), \(A_2(15,10;5) \ge 1024\), \(A_2(15,12;6) \ge 512\), \(A_2(15,14;7) \ge 256\), \(A_2(16,6;3) \ge 8192\), \(A_2(16,8;4) \ge 4096\), \(A_2(16,10;5) \ge 1048\), \(A_2(16,12;6) \ge 1024\), \(A_2(16,14;7) \ge 512\), \(A_2(16,16;8) \ge 256\), \(A_2(17,8;4) \ge 8192\), \(A_2(17,10;5) \ge 4096\), \(A_2(17,12;6) \ge 1048\), \(A_2(17,14;7) \ge 1024\), \(A_2(17,16;8) \ge 512\), \(A_2(18,10;5) \ge 8192\), \(A_2(18,12;6) \ge 4096\), \(A_2(18,14;7) \ge 1048\), \(A_2(18,16;8) \ge 1024\), \(A_2(18,18;9) \ge 512\), \(A_2(19,12;6) \ge 8192\), \(A_2(19,14;7) \ge 4096\), \(A_2(19,16;8) \ge 1048\), \(A_2(19,18;9) \ge 1024\), \(A_3(4,4;2) \ge 9\), \(A_3(5,4;2) \ge 27\), \(A_3(6,4;2) \ge 81\), \(A_3(6,4;3) \ge 729\), \(A_3(6,6;3) \ge 27\), \(A_3(7,4;2) \ge 243\), \(A_3(7,4;3) \ge 6561\), \(A_3(7,6;3) \ge 81\), \(A_3(8,4;2) \ge 729\), \(A_3(8,6;3) \ge 243\), \(A_3(8,6;4) \ge 6561\), \(A_3(8,8;4) \ge 81\), \(A_3(9,4;2) \ge 2187\), \(A_3(9,6;3) \ge 729\), \(A_3(9,8;4) \ge 243\), \(A_3(10,4;2) \ge 6561\), \(A_3(10,6;3) \ge 2187\), \(A_3(10,8;4) \ge 729\), \(A_3(10,10;5) \ge 243\), \(A_3(11,6;3) \ge 6561\), \(A_3(11,8;4) \ge 2187\), \(A_3(11,10;5) \ge 729\), \(A_3(12,8;4) \ge 6561\), \(A_3(12,10;5) \ge 2187\), \(A_3(12,12;6) \ge 729\), \(A_3(13,10;5) \ge 6561\), \(A_3(13,12;6) \ge 2187\), \(A_3(14,12;6) \ge 6561\), \(A_3(14,14;7) \ge 2187\), \(A_3(15,14;7) \ge 6561\), \(A_3(16,16;8) \ge 6561\), \(A_5(4,4;2) \ge 25\), \(A_5(5,4;2) \ge 125\), \(A_5(6,4;2) \ge 625\), \(A_5(6,6;3) \ge 125\), \(A_5(7,4;2) \ge 3125\), \(A_5(7,6;3) \ge 625\), \(A_5(8,6;3) \ge 3125\), \(A_5(8,8;4) \ge 625\), \(A_5(9,8;4) \ge 3125\), \(A_5(10,10;5) \ge 3125\), \(A_7(4,4;2) \ge 49\), \(A_7(5,4;2) \ge 343\), \(A_7(6,4;2) \ge 2401\), \(A_7(6,6;3) \ge 343\), \(A_7(7,6;3) \ge 2401\), \(A_7(8,8;4) \ge 2401\)
mdc codes: \(A_2(4,4) \ge 4\), \(A_2(5,4) \ge 9\), \(A_2(6,4) \ge 16\), \(A_2(6,4) \ge 64\), \(A_2(6,6) \ge 8\), \(A_2(7,4) \ge 32\), \(A_2(7,4) \ge 256\), \(A_2(7,6) \ge 16\), \(A_2(8,4) \ge 64\), \(A_2(8,4) \ge 1024\), \(A_2(8,4) \ge 4096\), \(A_2(8,6) \ge 32\), \(A_2(8,6) \ge 256\), \(A_2(8,8) \ge 16\), \(A_2(9,4) \ge 128\), \(A_2(9,4) \ge 4096\), \(A_2(9,6) \ge 64\), \(A_2(9,6) \ge 1024\), \(A_2(9,8) \ge 32\), \(A_2(10,4) \ge 256\), \(A_2(10,6) \ge 128\), \(A_2(10,6) \ge 4096\), \(A_2(10,8) \ge 64\), \(A_2(10,8) \ge 1024\), \(A_2(10,10) \ge 32\), \(A_2(11,4) \ge 512\), \(A_2(11,6) \ge 256\), \(A_2(11,6) \ge 16384\), \(A_2(11,8) \ge 128\), \(A_2(11,8) \ge 4096\), \(A_2(11,10) \ge 64\), \(A_2(12,4) \ge 1024\), \(A_2(12,6) \ge 512\), \(A_2(12,8) \ge 256\), \(A_2(12,10) \ge 128\), \(A_2(12,10) \ge 4096\), \(A_2(12,12) \ge 64\), \(A_2(13,4) \ge 2048\), \(A_2(13,6) \ge 1024\), \(A_2(13,8) \ge 512\), \(A_2(13,10) \ge 256\), \(A_2(13,12) \ge 128\), \(A_2(14,4) \ge 4096\), \(A_2(14,6) \ge 2048\), \(A_2(14,8) \ge 1024\), \(A_2(14,10) \ge 512\), \(A_2(14,12) \ge 256\), \(A_2(14,14) \ge 128\), \(A_2(15,4) \ge 8192\), \(A_2(15,6) \ge 4096\), \(A_2(15,8) \ge 1048\), \(A_2(15,10) \ge 1024\), \(A_2(15,12) \ge 512\), \(A_2(15,14) \ge 256\), \(A_2(16,6) \ge 8192\), \(A_2(16,8) \ge 4096\), \(A_2(16,10) \ge 1048\), \(A_2(16,12) \ge 1024\), \(A_2(16,14) \ge 512\), \(A_2(16,16) \ge 256\), \(A_2(17,8) \ge 8192\), \(A_2(17,10) \ge 4096\), \(A_2(17,12) \ge 1048\), \(A_2(17,14) \ge 1024\), \(A_2(17,16) \ge 512\), \(A_2(18,10) \ge 8192\), \(A_2(18,12) \ge 4096\), \(A_2(18,14) \ge 1048\), \(A_2(18,16) \ge 1024\), \(A_2(18,18) \ge 512\), \(A_2(19,12) \ge 8192\), \(A_2(19,14) \ge 4096\), \(A_2(19,16) \ge 1048\), \(A_2(19,18) \ge 1024\), \(A_3(4,4) \ge 9\), \(A_3(5,4) \ge 27\), \(A_3(6,4) \ge 81\), \(A_3(6,4) \ge 729\), \(A_3(6,6) \ge 27\), \(A_3(7,4) \ge 243\), \(A_3(7,4) \ge 6561\), \(A_3(7,6) \ge 81\), \(A_3(8,4) \ge 729\), \(A_3(8,6) \ge 243\), \(A_3(8,6) \ge 6561\), \(A_3(8,8) \ge 81\), \(A_3(9,4) \ge 2187\), \(A_3(9,6) \ge 729\), \(A_3(9,8) \ge 243\), \(A_3(10,4) \ge 6561\), \(A_3(10,6) \ge 2187\), \(A_3(10,8) \ge 729\), \(A_3(10,10) \ge 243\), \(A_3(11,6) \ge 6561\), \(A_3(11,8) \ge 2187\), \(A_3(11,10) \ge 729\), \(A_3(12,8) \ge 6561\), \(A_3(12,10) \ge 2187\), \(A_3(12,12) \ge 729\), \(A_3(13,10) \ge 6561\), \(A_3(13,12) \ge 2187\), \(A_3(14,12) \ge 6561\), \(A_3(14,14) \ge 2187\), \(A_3(15,14) \ge 6561\), \(A_3(16,16) \ge 6561\), \(A_5(4,4) \ge 25\), \(A_5(5,4) \ge 125\), \(A_5(6,4) \ge 625\), \(A_5(6,6) \ge 125\), \(A_5(7,4) \ge 3125\), \(A_5(7,6) \ge 625\), \(A_5(8,6) \ge 3125\), \(A_5(8,8) \ge 625\), \(A_5(9,8) \ge 3125\), \(A_5(10,10) \ge 3125\), \(A_7(4,4) \ge 49\), \(A_7(5,4) \ge 343\), \(A_7(6,4) \ge 2401\), \(A_7(6,6) \ge 343\), \(A_7(7,6) \ge 2401\), \(A_7(8,8) \ge 2401\)
KohnertKurz2008
Axel Kohnert and Sascha Kurz: “Construction of Large Constant Dimension Codes with a Prescribed Minimum Distance” Mathematical Methods in Computer Science. Lecture Notes in Computer Science, vol 5393. (2008): 31-42.
http://dx.doi.org/10.1007/978-3-540-89994-5_4
cdc codes: \(A_2(6,4;3) \ge 77\), \(A_2(7,4;3) \ge 304\), \(A_2(10,4;3) \ge 21483\), \(A_2(11,4;3) \ge 79833\), \(A_2(12,4;3) \ge 315315\), \(A_2(13,4;3) \ge 1154931\), \(A_2(14,4;3) \ge 4177665\)
mdc codes: \(A_2(6,4) \ge 77\)
Kurz2017
Sascha Kurz: “Upper bounds for partial spreads from divisible codes” The 13th International Conference on Finite Fields and their Applications (2017)
http://www.dma.unina.it/Fq13/Presentations/Media/talk_fq13_kurz.pdf
cdc constraints: special_case_2_13_10_5
Kurz20172
Sascha Kurz: “Improved upper bounds for partial spreads” Designs, Codes and Cryptography 85.1 (2017): 97–106
https://doi.org/10.1007/s10623-016-0290-8
cdc constraints: multicomponent, partial_spread_kurz_q2, partial_spread_kurz_q3
Kurz20173
Sascha Kurz: “Packing vector spaces into vector spaces” The Australasian Journal of Combinatorics 68.1 (2017): 122-130.
https://eref.uni-bayreuth.de/id/eprint/36705
cdc constraints: partial_spread_kurz16_28, partial_spread_kurz16_additional
Kurz2019
Sascha Kurz: “A note on the linkage construction for constant dimension codes” arXiv:1906.09780 (2019): 8.
https://arxiv.org/abs/1906.09780
cdc constraints: noted_linkage_special
Kurz20192
Sascha Kurz: “Subspaces intersecting in at most a point” Designs, Codes and Cryptography (to appear): 8.
https://arxiv.org/abs/1907.02728
cdc constraints: Kurz20192_Cor_4, Kurz20192_Eq_1, Kurz20192_Eq_3, Kurz20192_Eq_4, Kurz20192_Eq_5, Kurz20192_Prop_6
Kurz2020
Sascha Kurz: “Lifted codes and the multilevel construction for constant dimension codes” arXiv:2004.14241 (2020): 40.
https://arxiv.org/abs/2004.14241
cdc constraints: EF_Kurz2020_linkage_special, EF_Kurz2020_special
LiYeungCai2003
Shuo-Yen Robert Li, Raymond W. Yeung, and Ning Cai: “Linear network coding” IEEE Transactions on Information Theory 49.2 (2003): 371-381.
https://doi.org/10.1109/TIT.2002.807285
LiuChangFeng2018
Shuangqing Liu, Yanxun Chang, and Tao Feng: “Constructions for optimal Ferrers diagram rank-metric codes” IEEE Transactions on Information Theory 65.7 (2019): 4115-4130.
https://doi.org/10.1109/TIT.2019.2894401
LiuChangFeng2019
Shuangqing Liu, Yanxun Chang, and Tao Feng: “Parallel multilevel constructions for constant dimension codes” arXiv:1911.01878 (2019): 29.
https://arxiv.org/abs/1911.01878
cdc constraints: LiuChangFeng2019_Theo_2_6, LiuChangFeng2019_Theo_3_12, LiuChangFeng2019_Theo_3_14, LiuChangFeng2019_Theo_3_16, LiuChangFeng2019_Theo_3_18
MatevaTopalova2009
Zlatka T. Mateva and Svetlana T. Topalova: “Line spreads of PG(5, 2)” Journal of Combinatorial Designs 17.1 (2009): 90-102.
https://doi.org/10.1002/jcd.20198
cdc codes: \(A_2(6,4;2) \ge 21\)
MathonRoyle1995
Rudolf Mathon and Gordon F. Royle: “The translation planes of order 49” Designs, Codes and Cryptography 5.1 (1995): 57-72.
https://doi.org/10.1007/BF01388504
cdc codes: \(A_7(4,4;2) \ge 50\)
mdc codes: \(A_7(4,4) \ge 50\)
NastaseSissokho2017
Esmeralda Năstase and Papa Sissokho: “The maximum size of a partial spread II: Upper bounds” Discrete Mathematics 340.7 (2017): 1481-1487.
https://doi.org/10.1016/j.disc.2017.02.001
cdc constraints: partial_spread_NS_2_Theorem6, partial_spread_NS_2_Theorem7
NastaseSissokho20172
Esmeralda Năstase and Papa Sissokho: “The maximum size of a partial spread in a finite projective space” Journal of Combinatorial Theory, Series A 125 (2017): 353-362.
https://doi.org/10.1016/j.jcta.2017.06.012
cdc constraints: partial_spread_NS, partial_spread_NS_upper_bound
NiuYueWu2020
Yongfeng Niu, Qin Yue, and Yansheng Wu: “Several kinds of large cyclic subspace codes via Sidon spaces” Discrete Mathematics 343.5 (2020).
https://doi.org/10.1016/j.disc.2019.111788
NuffelenRompay2003
Cyriel Van Nuffelen and Kristel Van Rompay: “Upper bounds on the independence and the clique covering number” 4OR 1.1 (2003) 43-50.
https://doi.org/10.1007/s10288-002-0002-2
cdc constraints: prank
Segre1964
Beniamino Segre: “Teoria di Galois, fibrazioni proiettive e geometrie non desarguesiane.” Annali di Matematica Pura ed Applicata 64.1 (1964): 1-76
https://doi.org/10.1007/BF02410047
cdc constraints: spread
Shishkin2014
Alexander Shishkin: “A combined method of constructing multicomponent network codes” MIPT Proceedings 6.2 (2014) 188-194 (in Russian).
https://mipt.ru//upload/medialibrary/4fe/188-194.pdf
cdc constraints: greedy_multicomponent
ShishkinGabidulinPilipchuk2014
Alexander Shishkin, Ernst Gabidulin and Nina Pilipchuk: “On cardinality of network subspace codes” Proceeding of the Fourteenth Int. Workshop on Algebraic and Combinatorial Coding Theory (ACCT-XIV) (2014) 7.
http://www.moi.math.bas.bg/acct2014/a50.pdf
cdc constraints: greedy_multicomponent
SilbersteinEtzion2011
Natalia Silberstein and Tuvi Etzion: “Large constant dimension codes and lexicodes” Advances in Mathematics of Communications 5.2 (2011) 177-189.
http://dx.doi.org/10.3934/amc.2011.5.177
cdc codes: \(A_2(8,4;4) \ge 4589\), \(A_2(9,4;4) \ge 34944\), \(A_2(10,6;5) \ge 32890\), \(A_3(7,4;3) \ge 6691\)
SilbersteinTrautmann2015
Natalia Silberstein and Anna-Lena Trautmann: “Subspace Codes Based on Graph Matchings, Ferrers Diagrams, and Pending Blocks” IEEE Transactions on Information Theory 61.7 (2015): 3937-3953.
http://dx.doi.org/10.1109/TIT.2015.2435743
cdc constraints: construction_D, construction_ST_A_1, construction_ST_B, construction_ST_B_recursive, linkage_ST
Thomas1987
Simon Thomas: “Designs over finite fields” Geometriae Dedicata 24.2 (1987): 237–242.
http://arxiv.org/abs/1301.1918
Trautmann2013
Anna-Lena Trautmann: “A lower bound for constant dimension codes from multi-component lifted MRD codes” arXiv:1301.1918 (2013): 4.
http://arxiv.org/abs/1301.1918
cdc constraints: multicomponent
TrautmannRosenthal2010
Anna-Lena Trautmann and Joachim Rosenthal: “New Improvements on the Echelon-Ferrers Construction” Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems - MTNS Budapest, Hungary (2010): 405-408.
http://www.conferences.hu/mtns2010/proceedings/Papers/071_128.pdf
cdc constraints: echelon_ferrers, ef_computation
mdc constraints: echelon_ferrers, ef_computation
WangXingSafaviNaini2003
H. Wang, C. Xing, and R. Safavi-Naini: “Linear authentication codes: bounds and constructions” IEEE Transactions on Information Theory 49.4 (2003): 866–872.
https://doi.org/10.1109/TIT.2003.809567
cdc constraints: anticode
Xia2008
Shu-Tao Xia: “A Graham-Sloane Type Construction of Constant Dimension Codes” Network Coding, Theory and Applications, 2008. NetCod 2008. Fourth Workshop on (2008): 5.
https://doi.org/10.1109/NETCOD.2008.4476190
cdc constraints: graham_sloane
XiaFu2009
Shu-Tao Xia and Fang-Wei Fu: “Johnson type bounds on constant dimension codes” Designs, Codes and Cryptography 50.2 (2009): 163–172.
https://doi.org/10.1007/s10623-008-9221-7
cdc constraints: JohnsonLB, JohnsonLB_special, XiaFuJohnson1, johnson_1
XuChen2018
Liqing Xu and Hao Chen: “New Constant-Dimension Subspace Codes from Maximum Rank Distance Codes” IEEE Transactions on Information Theory 64.9 (2018): 6315-6319.
https://doi.org/10.1109/TIT.2018.2839596
cdc constraints: JohnsonLB_special, XuChen2018
ZhangGe2018
Tao Zhang and Gennian Ge: “Constructions of optimal Ferrers diagram rank metric codes” Designs, Codes and Cryptography 87 (2019): 107–121.
https://doi.org/10.1007/s10623-018-0491-4
ZhangJiangXia2011
Zong-Ying Zhang, Yong Jiang, and Shu-Tao Xia: “On the Linear Programming Bounds for Constant Dimension Codes” Network Coding (NetCod), 2011 International Symposium on (2011)
https://doi.org/10.1109/ISNETCOD.2011.5978916
cdc constraints: linear_programming_bound
Zumbragel2016
Jens Zumbrägel: “Designs and codes in affine geometry” arXiv:1605.03789 (2016)
https://arxiv.org/abs/1605.03789