Details for entry \(A_2(8,4;4)\)

Known codes

• 4801 Östergård, ALCOMA15 BraunOstergardWassermann2016 file
• 4590 GutierrezMolina2020
• 4589 SilbersteinEtzion2011
• 4420 GutierrezMolina2020
• 4096 LMRD KoetterKschischang2008, Gabidulin1985 file
• 2992 GutierrezMolina2015

Lower bounds

• CossidentePavese14_theorem43 ( ) : 4797
• construction_3 ( ) : 4797
• coset_construction ( ) : 4797
• CossidentePavese14_theorem38 ( ) : 4737
• CKMP2019_Cor_45 ( show
  (4,),(2,),(1,)
  ) : 4686
• LiuChangFeng2019_Theo_3_18 ( ) : 4642
• CKMP2019_Cor_42 ( (4, 4) ) : 4622
• CKMP2019_Lem_41 ( (4, 4) ) : 4622
• LiuChangFeng2019_Theo_2_6 ( ) : 4622
• generalized_linkage ( 4,0 ) : 4622
• generalized_linkage_multipleblocks ( show
  [4, 4],[0, 0]
  ) : 4622
• ChenHeWengXu2019_T31 ( ) : 4621
• ChenHeWengXu2019_T41 ( ) : 4621
• XuChen2018 ( ) : 4621
• ef_computation ( show
  [(0, 1, 2, 3), (0, 1, 4, 5), (0, 2, 4, 6), (1, 2, 4, 7), (2, 3, 4, 5), (0, 2, 5, 7), (0, 1, 6, 7), (1, 2, 5, 6), (1, 3, 4, 6), (0, 3, 5, 6), (0, 3, 4, 7), (1, 3, 5, 7), (2, 3, 6, 7), (4, 5, 6, 7)]
  ) : 4573
• pending_dots ( show
  optimal [(0, 1, 2, 3), (0, 1, 4, 5), (0, 1, 6, 7), (0, 2, 4, 6), (0, 2, 5, 7), (0, 3, 4, 7), (0, 3, 5, 6), (1, 2, 4, 7), (1, 2, 5, 6), (1, 3, 4, 6), (1, 3, 5, 7), (2, 3, 4, 5), (2, 3, 6, 7), (4, 5, 6, 7)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 4573 with optimal [(0, 1, 2, 3), (0, 1, 4, 5), (0, 1, 6, 7), (0, 2, 4, 6), (0, 2, 5, 7), (0, 3, 4, 7), (0, 3, 5, 6), (1, 2, 4, 7), (1, 2, 5, 6), (1, 3, 4, 6), (1, 3, 5, 7), (2, 3, 4, 5), (2, 3, 6, 7), (4, 5, 6, 7)])
  ) : 4573
• two_pivot_block_construction ( ) : 4368
• improved_linkage ( 4 ) : 4117
• multicomponent ( ) : 4113
• HKK_lemma_2_4_lower_bound ( ) : 2652
• JohnsonLB ( ) : 2261
• graham_sloane ( ) : 788
• coset_construction_parallelism_part ( show
  [(336, '(1,1), 2: 336'), (700, '(1,1), 4: 700'), (21, '(1,1), 6: 21'), (700, '(2,2), 4: 700')]
  ) : 700
• sphere_covering ( ) : 446

Upper bounds

• Ahlswede_Aydinian ( 0, 5 ) : 6477
• improved_johnson ( ) : 6477
• linear_programming_bound ( ) : 6477

Bound for codes containing the lifted MRD code

Do you have better bounds?