Cross-correlation distribution of p-ary m-sequence and its p+1 decimated sequences with shorter period

Abstract

In this paper, the cross-correlation distribution between a p-ary m-sequence s(t) and its p + 1 distinct decimated sequences s(dt + l) is derived. For an odd prime p, an even integer n, and d = p(k) + 1 with gcd(n, k) = 1, there are p + 1 distinct decimated sequences s(dt + l), 0 <= l < p + 1, for a p-ary m-sequence s(t) of period p(n) - 1 because gcd(d, p(n) - 1) = p + 1. The maximum magnitude of their cross-correlation values is 1 + P root p(n) if l equivalent to 0 mod p + 1 for n equivalent to 0 mod 4 or l equivalent to (p + 1)/2 mod p + 1 for n equivalent to 2 mod 4 and otherwise, 1 + root p(n). Also by using s(t) and s(dt + l), a new family of p-ary sequences of period p(n) - 1 is constructed, whose family size is p(n) and C-max is 1 + P root p(n).