Inequivalence of Difference Sets: On a Remark of Baumert

  • Padraig Ó Catháin
Keywords: difference sets


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 $t< 8$. We are not aware of a proof of this statement in the literature.

Three of the families discussed by Baumert have analogous constructions in non-cyclic 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.

Author Biography

Padraig Ó Catháin, University of Queensland
Postdoc in the School of Mathematics and Physics at the University of Queensland. Previously a PhD student at the National University of Ireland, Galway.
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