We give two constructions for semi-regular relative difference sets (RDSs) in groups whose order is not a prime power, where the order u of the forbidden subgroup is greater than 2. No such RDSs were previously known. We use examples from the first construction to produce semi-regular RDSs in groups whose 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.
Copyright © 1998, Springer. This article first appeared in Designs, Codes, and Cryptography: 13:2 (1998), 131-146.
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Davis, James A., Jonathan Jedwab, and Miranda Mowbray. "New Families of Semi-Regular Relative Difference Sets." Designs, Codes, and Cryptography 13, no. 2 (February 1998): 131-146. doi:10.1023/A:1008222227987.