Details for entry $$A_2(9,4;4)$$

Go to API

Lower bounds

• pending_dots (
optimal [(0, 1, 2, 3), (0, 1, 4, 5), (0, 1, 6, 7), (0, 2, 4, 6), (0, 2, 4, 8), (0, 2, 5, 6), (0, 2, 5, 7), (0, 3, 4, 6), (0, 3, 4, 7), (0, 3, 5, 7), (0, 3, 5, 8), (0, 3, 6, 8), (1, 2, 4, 7), (1, 2, 5, 8), (1, 3, 4, 8), (1, 3, 5, 6), (1, 3, 7, 8), (1, 4, 6, 8), (2, 3, 4, 5), (2, 3, 6, 7), (4, 5, 6, 7)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 37265 with optimal [(0, 1, 2, 3), (0, 1, 4, 5), (0, 1, 6, 7), (0, 2, 4, 6), (0, 2, 4, 8), (0, 2, 5, 6), (0, 2, 5, 7), (0, 3, 4, 6), (0, 3, 4, 7), (0, 3, 5, 7), (0, 3, 5, 8), (0, 3, 6, 8), (1, 2, 4, 7), (1, 2, 5, 8), (1, 3, 4, 8), (1, 3, 5, 6), (1, 3, 7, 8), (1, 4, 6, 8), (2, 3, 4, 5), (2, 3, 6, 7), (4, 5, 6, 7)])
) : 37265
• echelon_ferrers (
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: 36945 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)])
) : 36945
• ef_computation (
[(0, 1, 2, 3), (0, 1, 4, 5), (0, 2, 4, 6), (1, 3, 4, 6), (2, 3, 4, 5), (1, 2, 5, 6), (1, 2, 4, 7), (0, 2, 5, 7), (0, 1, 6, 7), (0, 3, 5, 6), (0, 3, 4, 7), (1, 3, 5, 7), (2, 3, 6, 8), (4, 5, 6, 7)]
) : 36945
• two_pivot_block_construction ( ) : 34944
• improved_linkage ( 4 ) : 33101
• multicomponent ( ) : 33025
• linkage_GLT ( 4 ) : 32769
• LMRD ( ) : 32768
• HKK_lemma_2_4_lower_bound ( ) : 11972
• graham_sloane ( ) : 6477
• improved_linkage ( 6 ) : 5377
• improved_linkage ( 7 ) : 5329
• improved_linkage ( 5 ) : 4117
• linkage_GLT ( 5 ) : 4097
• sphere_covering ( ) : 3556
• trivial_1 ( ) : 0

Bound for codes containing the lifted MRD code

(see EtzionSilberstein2012 and Heinlein2018 for details)
38969

Do you have better bounds?

You are welcome to contribute more information, clarifications, corrections and feature requests. If you want to contact us, press the “Contribute” button in the upper right corner or visit the About page. The preferred syntax for codes is GAP but feel free to submit any data in any format.