Details for entry \(A_2(10,6;5)\)

Known codes

• 32923 Heinlein2018 file
• 32890 SilbersteinEtzion2011
• 32841 EtzionSilberstein2009

Lower bounds

• ef_computation ( show
  [(0, 1, 2, 3, 4), (0, 1, 5, 6, 7), (0, 4, 5, 8, 9), (2, 3, 5, 7, 9), (2, 4, 6, 7, 8), (1, 3, 6, 8, 9)]
  ) : 32844
• greedy_multicomponent ( show
  [(0, 1, 2, 3, 4), (0, 1, 5, 6, 7), (0, 2, 5, 8, 9), (1, 3, 6, 8, 9), (2, 4, 6, 7, 8), (3, 4, 5, 7, 9)]
  ) : 32840
• pending_dots ( show
  optimal [(0, 1, 2, 3, 4), (0, 1, 5, 6, 7), (0, 4, 7, 8, 9), (1, 2, 5, 8, 9), (2, 3, 6, 7, 9), (3, 4, 5, 6, 8)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 32844 with optimal [(0, 1, 2, 3, 4), (0, 1, 5, 6, 7), (0, 4, 5, 8, 9), (1, 3, 6, 8, 9), (2, 3, 5, 7, 8), (2, 4, 6, 7, 9)])
  ) : 32839
• two_pivot_block_construction ( ) : 32832
• generalized_linkage ( 5,0 ) : 32777
• generalized_linkage_multipleblocks ( show
  [5, 5],[0, 0]
  ) : 32777
• CKMP2019_Cor_42 ( (5, 5) ) : 32769
• CKMP2019_Lem_41 ( (5, 5) ) : 32769
• LiuChangFeng2019_Theo_2_6 ( ) : 32769
• improved_linkage ( 5 ) : 32769
• multicomponent ( ) : 32769
• HKK_lemma_2_4_lower_bound ( ) : 8346
• JohnsonLB ( ) : 8109
• sphere_covering ( ) : 283
• graham_sloane ( ) : 105

Upper bounds

• Ahlswede_Aydinian ( 0, 9 ) : 38148
• improved_johnson ( ) : 38148
• linear_programming_bound ( ) : 40953

Bound for codes containing the lifted MRD code

Do you have better bounds?