Autocorrelation Function of a Family of Complex Sequences

Abstract

In 1984, R. A. Scholtz and L. R. Welch constructed a series of new binary se-quences which are called GMW sequences by using the trace function as follows: LetM, J be positive integers, J|M, α be a primitive element of the finite field GF(2~M), rbe a positive integer, 1≤r≤2~J, and(r, 2~J-1)=1. Then the sequence b=b(0)b(1)…b(n)…is called GMW sequence over GF(2). Here b(n)=tr_1~J(tr_J~Mα~n)~r, for n=0, 1, 2….