Some Notes on d-Form Functions with Difference-Balanced Property
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
New constructions of quaternary hadamard matrices
SETA'04 Proceedings of the Third international conference on Sequences and Their Applications
| Hi-index | 754.84 |
For a prime power q, we show that a cyclic relative difference set with parameters (qn-1/q-1,q-1,qn-1,qn-2) can be constructed from a d-homogeneous function from Fqn/{0} onto Fq with difference-balanced property, where Fqn is the finite field with qn elements. This construction method enables us to construct several new cyclic relative difference sets with parameters (pn-1/pl-1,pl-1,pn-l,pn-2l) from p-ary sequences of period pn-1 with ideal autocorrelation property introduced by Helleseth and Gong. Using a lifting idea, other new cyclic relative difference sets can be constructed from the Helleseth-Gong (HG) sequences. Also, the 3-ranks and the trace representation of the characteristic sequences of cyclic relative difference sets from a specific class of ternary HG sequences and ternary Lin sequences are derived.