New Families of Semi-Regular Relative Difference Sets

Authors:
James A. Davis;Jonathan Jedwab;Miranda Mowbray
Affiliations:
Department of Mathematics and Computer Science, University of Richmond, Virginia 23173, U.S.A. E-mail jdavis@richmond.edu;Hewlett-Packard Laboratories, Filton Road, Stoke Gifford, Bristol BS12 6QZ, U.K.;Hewlett-Packard Laboratories, Filton Road, Stoke Gifford, Bristol BS12 6QZ, U.K.
Venue:
Designs, Codes and Cryptography
Year:
1998

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Abstract

We give two constructions for semi-regular relativedifference sets (RDSs) in groups whose order is not a prime power,where the order u of the forbidden subgroup is greaterthan 2. No such RDSs were previously known. We use examples fromthe first construction to produce semi-regular RDSs in groupswhose order can contain more than two distinct prime factors.For u greater than 2 these are the first such RDSs,and for u=2 we obtain new examples.