Abelian Difference Sets Without Self-conjugacy
Document Type
Article
Publication Date
1998
Abstract
We obtain some results that are useful to the study of abelian difference sets and relative difference sets in cases where the self-conjugacy assumption does not hold. As applications we investigate McFarland difference sets, which have parameters of the form v=qd+1( qd+ qd-1 +...+ q+2) ,k=qd( qd+qd-1+...+q+1) , λ = qd ( q(d-1)+q(d-2)+...+q+1), where q is a prime power andd a positive integer. Using our results, we characterize those abelian groups that admit a McFarland difference set of order k-λ = 81. We show that the Sylow 3-subgroup of the underlying abelian group must be elementary abelian. Our results fill two missing entries in Kopilovich's table with answer “no”.
Repository Citation
Arasu, K. T.,
& Ma, S. L.
(1998). Abelian Difference Sets Without Self-conjugacy. Designs, Codes, and Cryptography, 15 (3), 223-230.
https://corescholar.libraries.wright.edu/math/568
DOI
10.1023/A:1008323907194
