On the minimum weights of binary LCD codes and ternary LCD codes

Makoto Araya; Masaaki Harada; Ken Saito

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arXiv · 1908.08661

On the minimum weights of binary LCD codes and ternary LCD codes

Makoto Araya·Masaaki Harada·Ken Saito

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Abstract

Linear complementary dual (LCD) codes are linear codes that intersect with their dual codes trivially. We study the largest minimum weight $d_2(n,k)$ among all binary LCD $[n,k]$ codes and the largest minimum weight $d_3(n,k)$ among all ternary LCD $[n,k]$ codes. The largest minimum weights $d_2(n,5)$ and $d_3(n,4)$ are partially determined. We also determine the largest minimum weights $d_2(n,n-5)$, $d_3(n,n-i)$ for $i \in \{2,3,4\}$, and $d_3(n,k)$ for $n \in \{11,12,\ldots,19\}$.

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Makoto Araya, Masaaki Harada, Ken Saito. 2020-11-18. On the minimum weights of binary LCD codes and ternary LCD codes. https://arxiv.org/abs/1908.08661

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