Cross-Correlation Distribution of p-ary m-Sequence and Its p + 1 Subsequences

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 les I < p + 1, for a p-ary m-sequence s(t) of period pⁿ - 1 since gcd(d, pⁿ -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 l+p radic pⁿ if I = 0 mod p + 1 for n = 0 mod 4 or I = (p + l)/2 mod p + 1 for n = 2 mod 4 and otherwise, 1 + radicpⁿ. Also by using s(t) and s(dt + I), a new family of p-ary sequences of period pⁿ -1 is constructed, whose family size is pⁿmiddot and C_max is 1+ pradicpⁿ.