Cross-correlation distribution of p-ary m-sequence and its p + 1 subsequences

Abstract

For an odd prime p, an even integer n, and d = pk + 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 pn - 1 since gcd(d, p n - 1) = p+ 1. 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. The maximum magnitude of their cross-correlation values is 1+p√pn if l = 0 mod p + 1 for n = 0 mod 4 or l = (p + l)/2 mod p + 1 for n = 2 mod 4 and otherwise, 1+ √pn Also by using s(t) and s(dt + l), a new family of p-ary sequences of period pn - 1 is constructed, whose family size is pn and Cmax is 1 + p√pn