Details for entry \(A_4(5,2)\)

Known codes

• 6139 optimal classified, number of isomorphism types: 1 HonoldKiermaierKurz20163

Exact bounds

• d2 ( ) : 6139

Lower bounds

• echelon_ferrers ( show
  optimal [(), (0, 1), (0, 1, 2, 3), (0, 1, 2, 4), (0, 1, 3, 4), (0, 2), (0, 2, 3, 4), (0, 3), (0, 4), (1, 2), (1, 2, 3, 4), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 6139 with optimal [(), (0, 1), (0, 1, 2, 3), (0, 1, 2, 4), (0, 1, 3, 4), (0, 2), (0, 2, 3, 4), (0, 3), (0, 4), (1, 2), (1, 2, 3, 4), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)])
  ) : 6139
• improved_cdc_lower_bound ( ) : 6139
• layer_construction ( ) : 6139
• cdc_lower_bound ( ) : 5797
• gilbert_varshamov ( ) : 405
• cdc_average_argument ( ) : 128
• trivial_4 ( ) : 2
• trivial_2 ( ) : 0

Upper bounds

• special_improved_cdc_upper_bound ( ) : 12276
• cdc_upper_bound ( ) : 12278
• improved_cdc_upper_bound ( ) : 12278
• relax_d ( ) : 12278
• trivial_3 ( ) : 12278

Do you have better bounds?