Cross-correlation distribution of p-ary m-sequence of period p(4k)-1 and its decimated sequences by (p(2k)+1/2)(2)

Abstract

For an odd prime p, n = 4k, and d = ((p(2k) +1)/2)(2), there are (p(2k) + 1)/2 distinct decimated sequences s(dt + l), 0 <= l < (p(2k) + 1)/2, of a p-ary m-sequence s(t) of period p(n) - 1 because gcd(d,p(n) - 1) = (p(2k) + 1)/2. In this paper, it is shown that the cross-correlation function between s(t) and s(dt + l), 0 <= l < (p(2k) + 1)/2, takes the values in {-1, -1 - root p(n), -1 + root p(n), -1 + 2 root p(n)} and their cross-correlation distribution is also derived.