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On the minimum weights of binary linear complementary dual codes
Cryptography and Communications ( IF 1.2 ) Pub Date : 2019-10-08 , DOI: 10.1007/s12095-019-00402-5
Makoto Araya , Masaaki Harada

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:

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[ nk ]码中最大的最小权重dnk)。我们确定dÑ,4)ñ ≡2,3,4,5,6,9,10,13(MOD 15),和dÑ,5),用于Ñ ≡3,4,5,7,11 ,19,20,22,26(mod 31)。与已知结果,合并的dÑķ)也被确定为Ñ ≤24。
更新日期:2019-10-08
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