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

中文翻译：

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关于二进制线性互补对偶码的最小权重

线性互补对偶代码（或具有互补对偶的代码）是与其对偶代码的交集不重要的代码。我们研究了所有二进制线性互补对偶[ n，k ]码中最大的最小权重d（n，k）。我们确定d（Ñ，4）ñ ≡2,3,4,5,6,9,10,13（MOD 15），和d（Ñ，5），用于Ñ ≡3,4,5,7,11 ，19,20，22,26（mod 31）。与已知结果，合并的d（Ñ，ķ）也被确定为Ñ ≤24。