Orthogonal designs, self‐dual codes, and the Leech lattice
Orthogonal designs, self‐dual codes, and the Leech lattice
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DOI：
10.1002/jcd.20046
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发表时间：
2005
影响因子：
0.7
通讯作者：
M. Harada;H. Kharaghani
中科院分区：
文献类型：
--
作者：
M. Harada;H. Kharaghani
对称设计和Hadamard矩阵用于构造二进制和三进制自对偶码。正交设计在构造大域上的自对偶码时是有用的。本文首先引入一个新的12阶数组，它适用于任何四个亲和循环矩阵的集合。我们应用一些12阶正交设计来构造大有限域上的新的自对偶码，通过构造A得到奇Leech格。© 2005威利期刊有限公司J Combin Designs 13：184-194，2005.
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. © 2005 Wiley Periodicals, Inc. J Combin Designs 13: 184–194, 2005.