HP Labs Technical Reports

A Unified Approach to Difference Sets with gcd (v,n) > 1

Davis, James A.; Jedwab, Jonathan

HPL-98-192

Keyword(s): difference sets; recursive; relative difference sets; symmetric designs

Abstract: Please Note. This abstract contains mathematical formulae which cannot be represented here. The five known families of difference sets whose parameters (v, k, , n) satisfy the condition gcd (v,n) > 1 are the McFarland, Spence, Davis-Jedwab, Hadamard and Chen families. We survey recent work which uses recursive techniques to unify these difference set families, placing particular emphasis on examples. This unified approach has also proved useful for studying semi- regular relative difference sets and for constructing new symmetric designs. Notes: James A. Davis, Department of Mathematics and Computer Science, University of Richmond, Virginia 23173, U.S.A.

25 Pages

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