Characterization and construction of h1-optimal binary linear codes related to LCD codes

초록

The hull of a linear code over finite fields is the intersection of the code and its dual, which was introduced by Assmus and Key to classify finite projective planes. A linear code C is called h & ell; -linear if C has & ell; -dimensional hull. Recently, several papers were devoted to related LCD codes over finite fields with size greater than 3 to h & ell; -linear codes with & ell;>= 1 . Therefore, the objective of this paper is to investigate an interesting but non-trivial problem, which is to study some properties of binary h1 -linear codes and establish their relation with binary LCD codes. Some interesting inequalities are thus obtained. Furthermore, we study the largest minimum distance done(n,k) among all binary h1 -linear [n, k] codes. We determine the largest minimum distances done(n,n-k) for k <= 5 and done(n,k) for k <= 4 or 14 <= n <= 24 . We partially determine the exact value of done(n,k) for k=5 or 25 <= n <= 30 .

키워드