Cross-correlation Distribution Of P-ary M-sequence And Its P + 1 Decimated Sequences With Shorter Period

摘要

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 (p~n) 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 + (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 (p~n).