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

Autor:	Araya, Makoto, Harada, Masaaki, Saito, Ken
Rok vydání:	2019
Předmět:	Computer Science - Information Theory Mathematics - Combinatorics
Druh dokumentu:	Working Paper
Popis:	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 $n \in \{11,12,\ldots,19\}$. Comment: 25 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1908.08661 Zobrazit plný text záznamu View this record from Arxiv