| 阶数为素数幂的一类整循环矩阵 |
| |
| 引用本文： | 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(1). |
| |
| 作者姓名： | 欧智明 韩书琴 |
| |
| 作者单位： | 北京邮电大学基础科学部(欧智明)，中国农业大学基础部(韩书琴) |
| |
| 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４ｒ（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＝ｐｒ（ｐ为素数）且元素为整数和循环矩阵Ｈ，若满足ＨＨＴ＝ｎＩ，则Ｈ的结构可完全确定．这种Ｈ可视为有限域Ｆｐｒ上的矩阵，因而得到了Ｆｐｒ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 |
On a Kind of Circulant Matrices with Their Order being a Prime Power |
| |
| Ou Zhiming.On a Kind of Circulant Matrices with Their Order being a Prime Power[J].Journal of Beijing University of Posts and Telecommunications,1998(1). |
| |
| Authors: | Ou Zhiming |
| |
| 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) and integral 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 . |
| |
| Keywords: | algebraic numbers circulant matrix hadamard matrix cyclotomic fields |
| 本文献已被 CNKI 等数据库收录！ |
