Classification and nonexistence results for linear codes with prescribed minimum distances

Titelangaben

Feulner, Thomas:
Classification and nonexistence results for linear codes with prescribed minimum distances.
In: Designs, Codes and Cryptography. Bd. 70 (2014) Heft 1-2 . - S. 127-138.
ISSN 1573-7586
DOI: https://doi.org/10.1007/s10623-012-9700-8

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Abstract

Starting from a linear [n,k,d]_q code with dual distance d⊥, we may construct an [n−d⊥, k−d⊥+1, ≥d]_q code with dual distance at least ceil(d⊥/q) using construction Y1. The inverse construction gives a rule for the classification of all [n,k,d]_q codes with dual distance d⊥ by adding d⊥ further columns to the parity check matrices of the smaller codes. Isomorph rejection is applied to guarantee a small search space for this iterative approach. Performing a complete search based on this observation, we are able to prove the nonexistence of linear codes for 16 open parameter sets [n,k,d]_q , q = 2, 3, 4, 5, 7, 8. These results imply 217 new upper bounds in the known tables for the minimum distance of linear codes and establish the exact value in 109 cases.