On difference matrices of coset type

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:120

Article

Hiramine, Yutaka¹  Suetake, Chihiro² 

[1] Kumamoto Univ, Fac Educ, Dept Math, Kumamoto, Japan

[2] Oita Univ, Fac Engn, Dept Math, Oita 8701192, Japan

关键词: Difference matrix;    Generalized Hadamard matrix;    Transversal design;   

DOI  :  10.1016/j.jcta.2012.08.008

来源: Elsevier

【 摘 要 】

A (u, k; lambda)-difference matrix H over a group U is said to be of coset type with respect to one of its rows, say w, whose entries are not equal, if it has the property that rw is also a row of H for any row r of H. In this article we study the structural property of such matrices with u(< k) a prime and show that u vertical bar lambda and, moreover, H contains u (u, k/u; lambda/u)-difference submatrices and is equivalent to a special kind of extension using them. Conversely, we also show that any set of u (u, k'; lambda')-difference matrices over U yields a (u, uk'; u lambda')-difference matrix of coset type over U. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free