Semi-regular relative difference sets with large forbidden subgroups |
| |
Authors: | Tao Feng Qing Xiang |
| |
Institution: | a School of Mathematical Sciences, Peking University, Beijing 100871, China b Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA |
| |
Abstract: | 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 2p2, and an abelian (4p,p,4p,4) relative difference set can only exist in the group . On the other hand, we construct a family of non-abelian relative difference sets with parameters (4q,q,4q,4), where q is an odd prime power greater than 9 and . When q=p is a prime, p>9, and , 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. |
| |
Keywords: | Gauss sum Mutually unbiased bases p-Ary bent function Relative difference set Semi-regular relative difference set |
本文献已被 ScienceDirect 等数据库收录! |
|