Orthogonal designs, self-dual codes, and the leech lattice

被引：7

作者：

Harada, M ^{[1
]}

Kharaghani, H

机构：

[1] Yamagata Univ, Dept Math Sci, Yamagata 9908560, Japan

[2] Univ Lethbridge, Dept Math & Comp Sci, Lethbridge, AB T1K 3M4, Canada

来源：

JOURNAL OF COMBINATORIAL DESIGNS | 2005年 / 13卷 / 03期

关键词：

orthogonal design; self-dual code; the Leech lattice;

D O I：

10.1002/jcd.20046

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Symmetric designs and Hadamard matrices are used to construct binary and ternary self-dual codes. Orthogonal designs are shown to be useful in construction of self-dual codes over large fields. In this paper, we first introduce a new array of order 12, which is suitable for any set of four amicable circulant matrices. We apply some orthogonal designs of order 12 to construct new self-dual codes over large finite fields, which lead us to the odd Leech lattice by Construction A. (c) 2005 Wiley Periodicals, Inc.

引用

页码：184 / 194

页数：11

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