Inequivalence of difference sets: on a remark of Baumert
Ó Catháin, PadraigORCID: 0000-0002-7963-9688
(2013)
Inequivalence of difference sets: on a remark of Baumert.
Electronic Journal of Combinatorics, 20
(1).
ISSN 1077-8926
An often cited statement of Baumert in his book Cyclic difference sets asserts
that four well known families of cyclic (4t − 1, 2t − 1, t − 1) difference sets are
inequivalent, apart from a small number of exceptions with t 6 8. We are not aware
of a proof of this statement in the literature.
Three of the families discussed by Baumert have analogous constructions in noncyclic groups. We extend his inequivalence statement to a general inequivalence
result, for which we provide a complete and self-contained proof. We preface our
proof with a survey of the four families of difference sets, since there seems to be
some confusion in the literature between the cyclic and non-cyclic cases.
2010 Mathematics Subject Classification: 05B20