Cross-correlation distribution of p-ary m-sequence of period p4k - 1 and its decimated sequences by (p2k+l\2)2

Abstract

For an odd prime p,n = 4k, and d = ((p2k+ l)/2)2, there are (p2k + 1)/2 distinct decimated sequences s(dt + l), 0 ≤ l < (p2k + l)/2, of a p-ary m-sequence s(t) of period p n - 1 because gcd(d, pn - 1) = (p2k + l)/2. In this paper, it is shown that the cross-correlation function between s(t) and s(dt + l), 0 ≤ l < (p2k + l)/2, takes the values in {-1, -1 - √pn, -1 + √pn, - 1 + 2√pn} and their cross-correlation distribution is also derived.