New Cyclic Difference Sets with Singer Parameters Constructed from d-Homogeneous Functions

摘要

In this paper, for a prime power q, new cyclic difference sets with Singer parameters ((q~n - 1/q - 1),(q~(n-1)- 1/q - 1), (q~(n-2) - 1/q - 1)) are constructed by using q-ary sequences (d-homogeneous functions) of period q~n - 1 and the generalization of GMW difference sets is proposed by combining the generation methods of d-form sequences and extended sequences. When q is a power of 3, new cyclic difference sets with Singer parameters ((q~n - 1/q - 1), (q~(n-1) - 1/q - 1), (q~(n-2) - 1/q - 1)) are constructed from the ternary sequences of period q~n - 1 with ideal autocorrelation introduced by Helleseth, Kumar, and Martinsen.