Equivalence classes of multiplicative central (pn, pn, pn, 1)-relative difference sets

Authors:
D. G. Farmer;K. J. Horadam
Affiliations:
Mathematical Sciences, SMGS, RMIT University---City Campus, Melbourne, Australia VIC 3001;Mathematical Sciences, SMGS, RMIT University---City Campus, Melbourne, Australia VIC 3001
Venue:
Cryptography and Communications
Year:
2011

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Abstract

We show by explicit construction that the equivalence classes of multiplicative central (p n , p n , p n , 1)-RDSs relative to ${\mathbb Z}_p^n$ in groups E with $E/{\mathbb Z}_p^n \cong {\mathbb Z}_p^n$ are in one-to-one correspondence with the strong isotopism classes of presemifields of order p n . We also show there are 1,446 equivalence classes of central (16, 16, 16, 1)-RDS relative to ${\mathbb Z}_2^4$ , in groups E for which $E/{\mathbb Z}_2^4 \cong {\mathbb Z}_2^4$ . Only one is abelian.