an:06008447
Zbl 1234.05047
Farmer, D. G.; Horadam, K. J.
Equivalence classes of multiplicative central \((p^{n}, p^{n}, p^{n}, 1)\)-relative difference sets
EN
Cryptogr. Commun. 3, No. 1, 17-28 (2011).
00295730
2011
j
05B10 05B25
relative difference set; equivalence class; presemifield
Summary: 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 \(E/\mathbb Z_{p}^n\cong \mathbb Z_p^n\) arein 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.