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.
http://ieeexplore.ieee.org/document/5191396/
cdc constraints: Ahlswede_Aydinian
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.
http://link.springer.com/article/10.1007%2FBF01187370
cdc constraints: spread
BachocPassuelloVallentin2013
Christine Bachoc, Alberto Passuello, and Frank Vallentin: “Bounds for projective codes from semidefinite programming” Advances of Mathematics in Communications 7 (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.
http://link.springer.com/article/10.1007%2FBF01215286
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
BraunEtzionOstergardVardyWassermann2013
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: \(A_2(13,4;3) \ge 1597245\)
BraunOstergardWassermann2016
Michael Braun, Patric R. J. Östergård, and Alfred Wassermann: “New Lower Bounds for Binary Constant-Dimension Subspace Codes” Experimental Mathematics (2016): 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: \(A_2(7,4;3) \ge 329\), \(A_2(8,4;3) \ge 1312\), \(A_2(11,4;3) \ge 92411\), \(A_2(12,4;3) \ge 385515\), \(A_2(14,4;3) \ge 5996178\)
CossidentePavese2014
Antonio Cossidente and Francesco Pavese: “Subspace codes in PG(2n-1,q)” arXiv:1411.3601 (2014): 26, (to appear in Combinatorica).
http://arxiv.org/abs/1411.3601
cdc constraints: CossidentePavese14_theorem311, CossidentePavese14_theorem38, CossidentePavese14_theorem43
CossidentePavese2015
Antonio Cossidente and Francesco Pavese: “Veronese subspace codes” Designs, Codes and Cryptography (2015): 1-13.
http://link.springer.com/article/10.1007/s10623-015-0166-3
cdc constraints: CossidentePavese_n6_d4_k3
CossidentePaveseStorme2016
Antonio Cossidente, Francesco Pavese, and Leo Storme: “Optimal subspace codes in PG(4,q)” in preparartion.

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.
http://www.sciencedirect.com/science/article/pii/0097316592900653
Dembowski1968
Peter Dembowski: “Finite Geometries: Reprint of the 1968 edition” Springer Science & Business Media (2012)
http://www.springer.com/gp/book/9783540617860
cdc constraints: spread
Dempwolff1994
Ulrich Dempwolff: “Translation planes of order 27” Designs, Codes and Cryptography 4.2 (1994): 105-121.
http://link.springer.com/article/10.1007%2FBF01578865
cdc codes: \(A_3(6,6;3) \ge 28\)
DempwolffReifart1983
Ulrich Dempwolff and A. Reifart: “The classification of the translation planes of order 16, I” Geometriae Dedicata 15.2 (1983): 137-153.
http://link.springer.com/article/10.1007%2FBF00147760
DrakeFreeman1979
David A. Drake and J. W. Freeman: “Partial t-spreads and group constructible (s,r,μ)-nets” Journal of Geometry 13 (1979): 210-216.
http://link.springer.com/article/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.
http://link.springer.com/article/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 constraints: special_cases_lower, special_cases_upper
mdc codes: \(A_2(6,4) \ge 77\)
EtzionSilberstein2009
Tuvi Etzion and Natalia Silberstein: “Error-Correcting Codes in Projective Spaces via Rank-Metric Codes and Ferrers Diagrams” Information Theory, IEEE Transactions on 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
EtzionSilberstein2012
Tuvi Etzion and Natalia Silberstein: “Codes and Designs Related to Lifted MRD Codes” Information Theory, IEEE Transactions on 59.2 (2012): 1004-1017.
http://dx.doi.org/10.1109/TIT.2012.2220119
mdc codes: \(A_2(7,3) \ge 584\)
EtzionVardy2011
Tuvi Etzion, and Alexander Vardy: “Error-Correcting Codes in Projective Space” Information Theory, IEEE Transactions on 57.2 (2011): 1165-1173.
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5695131
cdc constraints: anticode, johnson_1, johnson_2, partial_spread_3, partial_spread_5
mdc constraints: gilbert_varshamov, ilp
mdc codes: \(A_2(5,3) \ge 18\), \(A_2(6,3) \ge 85\)
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.
http://www.sciencedirect.com/science/article/pii/0097316586900634?via%3Dihub
cdc constraints: anticode
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
GordonShawSoicher2004
Neil A. Gordon, Ron Shaw, and Leonard H. Soicher: “Classification of partial spreads in PG (4, 2)” (2004): 63.
http://www.maths.qmul.ac.uk/~leonard/partialspreads/PG42new.pdf
cdc codes: \(A_2(5,4;2) \ge 9\)
GorlaRavagnani2014
Elisa Gorla and Alberto Ravagnani: “Subspace Codes from Ferrers Diagrams” arXiv:1405.2736 (2014) 16.
http://arxiv.org/abs/1405.2736
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: \(A_2(8,4;4) \ge 2992\), \(A_2(8,4;4) \ge 4590\), \(A_2(10,4;3) \ge 21483\), \(A_2(10,10;5) \ge 33\)
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://www.jstor.org/stable/2001913
HeinleinKiermaierKurzWassermann2016
Daniel Heinlein, Michael Kiermaier, Sascha Kurz, and Alfred Wassermann: “Symmetry groups for projective and affine structures in the binary Fano setting” in preparation (2016)

HeinleinKurz2015
Daniel Heinlein and Sascha Kurz: “Coset Construction for Subspace Codes” arXiv:1512.07634 (2015) 17.
http://arxiv.org/abs/1512.07634
cdc constraints: coset_construction, coset_construction_parallelism_part
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
Hirschfeld1998
J. W. P. Hirschfeld: “Projective geometries over finite fields” The Clarendon Press Oxford University Press New York, second edition (1998).

HonoldKiermaier2015
Thomas Honold and Michael Kiermaier: “On putative q-Analogues of the Fano Plane and Related Combinatorial Structures” arXiv:1504.06688 (2015) 37.
http://arxiv.org/abs/1504.06688
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://arxiv.org/abs/1311.0464
cdc constraints: HonoldKiermaierKurz_n6_d4_k3
cdc codes: \(A_2(6,4;3) \ge 77\)
HonoldKiermaierKurz20152
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 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: d2, d4_cdc, improved_cdc_lower_bound, improved_cdc_upper_bound, layer_construction, neqdeven, neven_deqnm1, nodd_deqnm1, nodd_deqnm2, nodd_deqnm2_e, nodd_deqnm2_l, nodd_deqnm2_u, special_cases_upper_notderived
mdc codes: \(A_2(2,2) \ge 3\), \(A_2(3,2) \ge 8\), \(A_2(4,2) \ge 37\), \(A_2(4,3) \ge 5\), \(A_2(4,4) \ge 5\), \(A_2(5,2) \ge 187\), \(A_2(5,3) \ge 18\), \(A_2(5,4) \ge 9\), \(A_2(6,2) \ge 1521\), \(A_2(6,3) \ge 104\), \(A_2(6,4) \ge 77\), \(A_2(6,5) \ge 9\), \(A_2(6,6) \ge 9\), \(A_2(7,2) \ge 14606\), \(A_2(7,3) \ge 593\), \(A_2(7,5) \ge 34\), \(A_2(7,6) \ge 17\), \(A_2(8,8) \ge 17\), \(A_3(4,4) \ge 10\), \(A_3(6,6) \ge 28\), \(A_4(4,4) \ge 17\), \(A_5(4,4) \ge 26\), \(A_7(4,4) \ge 50\), \(A_2(3,3) \ge 2\), \(A_2(5,5) \ge 2\), \(A_2(7,7) \ge 2\), \(A_2(9,9) \ge 2\), \(A_2(11,11) \ge 2\), \(A_2(13,13) \ge 2\), \(A_2(15,15) \ge 2\), \(A_2(17,17) \ge 2\), \(A_2(19,19) \ge 2\), \(A_3(3,3) \ge 2\), \(A_3(5,5) \ge 2\), \(A_3(7,7) \ge 2\), \(A_3(9,9) \ge 2\), \(A_3(11,11) \ge 2\), \(A_3(13,13) \ge 2\), \(A_3(15,15) \ge 2\), \(A_3(17,17) \ge 2\), \(A_3(19,19) \ge 2\), \(A_4(3,3) \ge 2\), \(A_4(5,5) \ge 2\), \(A_4(7,7) \ge 2\), \(A_4(9,9) \ge 2\), \(A_4(11,11) \ge 2\), \(A_4(13,13) \ge 2\), \(A_4(15,15) \ge 2\), \(A_4(17,17) \ge 2\), \(A_4(19,19) \ge 2\), \(A_5(3,3) \ge 2\), \(A_5(5,5) \ge 2\), \(A_5(7,7) \ge 2\), \(A_5(9,9) \ge 2\), \(A_5(11,11) \ge 2\), \(A_5(13,13) \ge 2\), \(A_5(15,15) \ge 2\), \(A_5(17,17) \ge 2\), \(A_5(19,19) \ge 2\), \(A_7(3,3) \ge 2\), \(A_7(5,5) \ge 2\), \(A_7(7,7) \ge 2\), \(A_7(9,9) \ge 2\), \(A_7(11,11) \ge 2\), \(A_7(13,13) \ge 2\), \(A_7(15,15) \ge 2\), \(A_7(17,17) \ge 2\), \(A_7(19,19) \ge 2\), \(A_8(3,3) \ge 2\), \(A_8(5,5) \ge 2\), \(A_8(7,7) \ge 2\), \(A_8(9,9) \ge 2\), \(A_8(11,11) \ge 2\), \(A_8(13,13) \ge 2\), \(A_8(15,15) \ge 2\), \(A_8(17,17) \ge 2\), \(A_8(19,19) \ge 2\), \(A_9(3,3) \ge 2\), \(A_9(5,5) \ge 2\), \(A_9(7,7) \ge 2\), \(A_9(9,9) \ge 2\), \(A_9(11,11) \ge 2\), \(A_9(13,13) \ge 2\), \(A_9(15,15) \ge 2\), \(A_9(17,17) \ge 2\), \(A_9(19,19) \ge 2\)
HonoldKiermaierKurz2016
Thomas Honold, Michael Kiermaier, and Sascha Kurz: “Classification of large partial plane spreads in PG(6, 2) and related combinatorial objects” arXiv:1606.07655
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
https://arxiv.org/abs/1611.06328
cdc constraints: partial_spread_HKK16_T10
cdc codes: \(A_2(8,6;3) \ge 34\)
KoetterKschischang2008
Ralf Koetter and Frank R. Kschischang: “Coding for Errors and Erasures in Random Network Coding” Information Theory, IEEE Transactions on 54.8 (2008): 3579-3591.
http://dx.doi.org/10.1109/TIT.2008.926449
cdc constraints: lin_poly, singleton, sphere_covering, sphere_packing
KohnertKurz2008
Axel Kohnert and Sascha Kurz: “Construction of large constant dimension codes with a prescribed minimum distance” Lecture Notes Computer Science 5393 (2008): 31-42
http://dx.doi.org/10.1007/978-3-540-89994-5_4
cdc codes: \(A_2(6,4;3) \ge 77\), \(A_2(7,4;3) \ge 304\)
mdc codes: \(A_2(6,4) \ge 77\)
Kurz2015
Sascha Kurz: “Improved upper bounds for partial spreads” arXiv:1512.04297 (2015) 8.
http://arxiv.org/abs/1512.04297
cdc constraints: partial_spread_kurz_q2, partial_spread_kurz_q3
Kurz2016
Sascha Kurz: “Upper Bounds for Partial Spreads” arXiv:1606.08581 (2016): 3.
http://arxiv.org/abs/1606.08581
cdc constraints: partial_spread_kurz16_28, partial_spread_kurz16_additional
Kurz2017
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
MatevaTopalova2009
Zlatka T. Mateva and Svetlana T. Topalova: “Line spreads of PG(5, 2)” J. Combin. Designs 17 (2009): 90-102
https://www.researchgate.net/profile/Zlatka_Mateva/publication/227727062_Line_spreads_of_PG%285_2%29/links/0f317534cc69e1f1b6000000.pdf
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.
http://link.springer.com/article/10.1007/BF01388504
NastaseSissokho2016
Esmeralda Năstase and Papa Sissokho: “The maximum size of a partial spread in a finite projective space” arXiv:1605.04824 (2016): 9.
http://arxiv.org/abs/1605.04824
cdc constraints: partial_spread_NS, partial_spread_NS_upper_bound
NastaseSissokho20162
Esmeralda Năstase and Papa Sissokho: “The maximum size of a partial spread II: Upper Bounds” arXiv:1606.09208 (2016): 9.
http://arxiv.org/abs/1606.09208
cdc constraints: partial_spread_NS_2_Theorem6, partial_spread_NS_2_Theorem7
Shishkin2014
Александр Шишкин: “Комбинированный метод построения многокомпонентных сетевых кодов” Труды МФТИ 6.2 (2014) 188-194.
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
SilbersteinEtzion2010
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: \(A_2(8,4;4) \ge 4589\), \(A_2(9,4;4) \ge 34944\), \(A_2(10,6;5) \ge 32890\), \(A_3(7,4;3) \ge 6691\)
SilbersteinEtzion2011
Natalia Silberstein and Tuvi Etzion: “Codes and Designs Related to Lifted MRD Codes” Information Theory, IEEE Transactions on 59.2 (2011): 1004-1017.
http://dx.doi.org/10.1109/TIT.2012.2220119
cdc constraints: construction_1, construction_2, construction_3, pending_dots
SilbersteinTrautmann2014
Natalia Silberstein and Anna-Lena Trautmann: “Subspace Codes Based on Graph Matchings, Ferrers Diagrams, and Pending Blocks” Information Theory, IEEE Transactions on 61.7 (2015): 3937-3953.
http://dx.doi.org/10.1109/TIT.2015.2435743
cdc constraints: construction_ST_A_1, construction_ST_B, linkage_ST
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
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.
http://ieeexplore.ieee.org/abstract/document/1193797/
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.
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=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.
http://link.springer.com/article/10.1007/s10623-008-9221-7
cdc constraints: XiaFuJohnson1