On the Cross-Correlation of a p-Ary m-Sequence of Period p(2m)-1 and Its Decimated Sequences by (p(m)+1)(2)/2(p+1)

Abstract

In this paper, for an odd prime p, we investigate into the cross-correlation of a p-ary m-sequence m(t) of period p(n) - 1 and its d-decimated sequences m(dt + l), 0 <= l < p(m)+1/2, where d = (p(m)+1)(2)/2(p+1), n = 2m, and m is an odd integer. There are p(m)+1/2 distinct decimated sequences m(dt + l) since gcd(d, p(n) - 1) = (p(m)+1)/2. It is shown that the magnitude of the cross-correlation values is upper bounded by p+1/2 p(n/2) + 1. We also construct the sequence family F from these sequences, where the family size is p(m) and the correlation magnitude is upper bounded by p+1/2 p(n/2) + 1.