Hadamard matrices related to a certain series of ternary self-dual codes

被引：4

作者：

Araya, Makoto ^{[1
]}

Harada, Masaaki ^{[2
]}

Momihara, Koji ^{[3
]}

机构：

[1] Shizuoka Univ, Dept Comp Sci, Hamamatsu, Shizuoka 4328011, Japan

[2] Tohoku Univ, Res Ctr Pure & Appl Math, Grad Sch Informat Sci, Sendai, Miyagi 9808579, Japan

[3] Kumamoto Univ, Fac Adv Sci & Technol, Div Nat Sci, Kumamoto 8608555, Japan

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2023年 / 91卷 / 03期

关键词：

Self-dual code; Ternary extremal self-dual code; Hadamard matrix; LENGTH; CLASSIFICATION;

D O I：

10.1007/s10623-022-01127-y

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In 2013, Nebe and Villar gave a series of ternary self-dual codes of length 2(p+1) for a prime p congruent to 5 modulo 8. As a consequence, the third ternary extremal self-dual code of length 60 was found. We show that these ternary self-dual codes contain codewords which form a Hadamard matrix of order 2(p+1) when p is congruent to 5 modulo 24. In addition, we show that the ternary self-dual codes found by Nebe and Villar are generated by the rows of the Hadamard matrices. We also demonstrate that the third ternary extremal self-dual code of length 60 contains at least two inequivalent Hadamard matrices.

引用

页码：795 / 805

页数：11

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