Relative (p(a), p(b), p(a), p(a-b))-difference sets: A unified exponent bound and a local ring construction

Authors
Ma, SL Schmidt, B
Citation
Sl. Ma et B. Schmidt, Relative (p(a), p(b), p(a), p(a-b))-difference sets: A unified exponent bound and a local ring construction, FINITE F T, 6(1), 2000, pp. 1-22
Citations number
31
Categorie Soggetti
Mathematics
Journal title
FINITE FIELDS AND THEIR APPLICATIONS
ISSN journal
10715797 → ACNP
Volume
6
Issue
1
Year of publication
2000
Pages
1 - 22
Database
ISI
SICI code
1071-5797(200001)6:1<1:R(PPPS>2.0.ZU;2-Y
Abstract
We show that for an odd prime p the exponent of an abelian group of order p (a+b) containing a relative (p(a), p(b), p(a), p(a-b))-difference set canno t exceed p([a/2] + 1). Furthermore, we give a new local ring construction o f relative (q(2u), q, q(2u), q(2u-1))-difference sets for prime powers q. F inally, we discuss an important open case concerning the existence of abeli an relative (p(a), p, p(a), p(a-1))-difference sets. (C) 2000 Academic Pres s.