New Cyclic Relative Difference Sets Constructed From d-Homogeneous Functions With Difference-Balanced Property.

For a prime power q, we show that a cyclic relative difference set with parameters (qn-1/q-1, q-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-1, pn-2t) 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. [ABSTRACT FROM AUTHOR]