Semi-regular relative difference sets with large forbidden subgroups

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:115

Article

Feng, Tao¹  Xiang, Qing² 

[1] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China

[2] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

关键词: Gauss sum;    Mutually unbiased bases;    p-Ary bent function;    Relative difference set;    Semi-regular relative difference set;   

DOI  :  10.1016/j.jcta.2008.02.003

来源: Elsevier

【 摘 要 】

Motivated by a connection between semi-regular relative difference sets and mutually unbiased bases, we study relative difference sets with parameters (m, n, m, m/n) in groups of non-prime-power orders. Let p be an odd prime. We prove that there does not exist a (2p. p, 2p, 2) relative difference set in any group of order 2p(2), and an abelian (4p, p, 4p, 4) relative difference set can only exist in the group Z(2)(2) X Z(3)(2). On the other hand, we construct a family of 2 3 non-abelian relative difference sets with parameters (4q, q, 4q, 4), where q is an odd prime power greater than 9 and q 1 (mod 4). When q = p is a prime, p > 9, and p 1 (mod 4), the (4p, p, 4p. 4) non-abelian relative difference sets constructed here are genuinely non-abelian in the sense that there does not exist an abelian relative difference set with the same parameters. (C) 2008 Elsevier Inc. All rights reserved.

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