On the minimum weights of binary linear complementary dual codes

Abstract

Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. We study the largest minimum weight $d(n,k)$ among all binary linear complementary dual $[n,k]$ codes. We determine $d(n,4)$ for $n\equiv 2,3,4,5,6,9,10,13(\mathrm{mod}15)$, and $d(n,5)$ for $n\equiv 3,4,5,7,11,19,20,22,26(\mathrm{mod}31)$. Combined with known results, the values $d(n,k)$ are also determined for $n\le 24$.

arXiv comment21 pages

References in corpus (2)

• LCD codes over ${\mathbb{F}}_q$ are as good as linear codes for q at least four
• Binary linear complementary dual codes

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