阶数为素数幂的一类整循环矩阵

北京邮电大学学报 ›› 1998, Vol. 21 ›› Issue (1): 7-11.

阶数为素数幂的一类整循环矩阵

欧智明¹,韩书琴²

¹北京邮电大学基础科学部, 北京 100876; 34岁, 男, 教授;²中国农业大学基础部, 北京 100083

收稿日期:1997-02-20 出版日期:1998-01-10

On a Kind of Circulant Matrices with#br# Their Order being a Prime Power

Ou Zhiming¹,Han Shuqin²

¹Department of Basic Science, Beijing University of Posts and Telecommunications, Beijing 100876;²Department of Basic Courses, Agricultural University of China, Beijing 100083

Received:1997-02-20 Online:1998-01-10

摘要/Abstract

摘要： 在循环哈达玛矩阵的研究中, 引进了代数数论中的素理想分解方法, 证明了阶数为4^r(r＞1)的循环哈达玛矩阵是不存在的, 并给出了全部4阶循环哈达玛矩阵.对于阶数为n=p^r(p为素数)且元素为整数和循环矩阵H,若满足HH^{T=nI, 则H的结构可完全确定.这种H可视为有限域F_p^r上的矩阵, 因而得到了F_p^r上一种正交码的构造.}

关键词: 代数整数, 循环矩阵, 哈达玛矩阵, 分园域

Abstract: In the research of Hadamard matrices, by using the method of factorization of prime ideals in algebraic number theory, we proved that circulant Hadamard matrices with order 4^r(r＞1) do not exist, and obtained the Hadamard matrices with order 4.For a circulant matrix H satisfying HH^{T=nI with order p^r (p is a prime) andintegral elements, we completely determined the structure of H.Such matrices can be viewed as matrices over finite field F_p^r, thus we obtained the construction of a sort of orthogonal codes over F_p^r.}

Key words: algebraic numbers, circulant matrix, hadamard matrix, cyclotomic fields

中图分类号:

O151.21

欧智明,韩书琴. 阶数为素数幂的一类整循环矩阵[J]. 北京邮电大学学报, 1998, 21(1): 7-11.

Ou Zhiming,Han Shuqin. On a Kind of Circulant Matrices with#br# Their Order being a Prime Power[J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 1998, 21(1): 7-11.