Abstract
Relative Difference Sets with the parameters k = nλ have been constructed many ways (see (Davis, forthcoming; Elliot and Butson 1966; and Jungnickel 1982)). This paper proves a result on building new RDS by taking products of others (much like (Dillon 1985)), and this is applied to several new examples (primarily involving (p i, p j, p i, p i−j)).
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References
Davis, J.A. (forthcoming). Construction of relative difference sets in p-groups. Discrete Mathematics.
Dillon, J.F. 1985. Variations on a scheme of McFarland for noncyclic difference sets. J. Combin. Theory Ser. A 40: 9–21.
Elliot, J.E.H., and Butson, A.T. 1966. Relative difference sets. Illinois J. Math. 10: 517–531.
Jungnickel, D. 1982. On automorphism groups of divisible designs. Can. J. Math. 34: 257–297.
Turyn, R.J. 1984. A special class of Williamson matrices and difference sets. J. Combin. Theory Ser. A 36: 111–115.
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Communicated by D. Jungnickel
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Davis, J.A. A note on products of Relative Difference Sets. Des Codes Crypt 1, 117–119 (1991). https://doi.org/10.1007/BF00157615
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DOI: https://doi.org/10.1007/BF00157615