Inequivalence of Difference Sets: On a Remark of Baumert
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.
2013 ◽
Vol E96.A
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pp. 171-176
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1999 ◽
Vol 87
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pp. 74-119
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1977 ◽
Vol 16
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pp. 361-369
2000 ◽
Vol 70
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pp. 357-367
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1975 ◽
Vol 19
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pp. 177-191
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