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基于有限阿贝尔群上Jacket矩阵的构造方法

发表时间:2012-11-30  浏览量:1538  下载量:703
全部作者: 周慧珠,郭迎,李门浩
作者单位: 中南大学信息科学与工程学院;韩国全北国立大学信息与通信学院
摘 要: 在国内外研究的基础上,提出了一种基于有限阿贝尔群构造出的Jacket矩阵,利用矩阵Kronecker积的性质,构造出任意高阶的Jacket矩阵,大大降低了计算复杂度,也对有限域上矩阵构建的研究工作做出了贡献。同时,讨论了方阵和非方阵2种情况,有助于各种形式矩阵的构造。为了能快速地构建出高阶的Jacket矩阵,提出一种基于Kronecker积的快速Jacket变换算法,减少了矩阵计算的运算量。
关 键 词: 信息处理技术;Jacket矩阵;Hadamard矩阵;有限阿贝尔群;Kronecker积;快速Jacket变换算法
Title: A new construction of Jacket matrix based on finite Abelian group
Author: ZHOU Huizhu, GUO Ying, LEE Moonho
Organization: School of Information Science and Engineering, Central South University; Institute of Information and Communication, Chonbuk National University
Abstract: In this paper, an original construction of Jacket matrix motivated by the element inverse property of the center weighted Hadamard matrix is suggested with suitably chosen characters on finite Abelian group. Based on Fermat’s little theorem, the objective Jacket matrix is obtained. The present matrix is an extension of the conventional Jacket matrices on the Galois field. It is a contribution to a problem of searching for an extended family of Jacket matrices on finite Abelian 25 group. In order to get different patterns of Jacket matrices, the conditions of square and non-square are both discussed. Exploiting the well-known Kronecker product of sparse matrices and the relationship of successively lower-order Jacket matrices, a fast construction approach for large size Jacket matrices is proposed. The result indicates the presented fast algorithm performs quite well at decreasing the computation complexity.
Key words: information processing technique; Jacket matrix; Hadamard matrix; finite Abelian group; Kronecker product; fast Jacket decomposition algorithm
发表期数: 2012年11月第22期
引用格式: 周慧珠,郭迎,李门浩. 基于有限阿贝尔群上Jacket矩阵的构造方法[J]. 中国科技论文在线精品论文,2012,5(22):2167-2175.
 
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