Relative Difference Sets with the parameters (2a, 2b, 2a, 2a-b) have been constructed many ways (see , , , , and  for examples). This paper modifies an example found in  to construct a family of relative difference sets in 2-groups that gives examples for b = 2 and b = 3 that have a lower rank than previous examples. The Simplex code is used in the construction.
Copyright © 1997, Springer. This article first appeared in Designs, Codes, and Cryptography: 11:3 (1997), 267-277.
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Davis, James A., and Surinder K. Sehgal. "Using the Simplex Code to Construct Relative Difference Sets in 2-groups." Designs, Codes, and Cryptography 11, no. 3 (July 1997): 267-77. doi: 10.1023/A:1008246212180.