Cross-Correlation Distribution of p-ary m-Sequence and Its p + 1 Subsequences
Eun-Young Seo, Young Sik Kim, Jong‐Seon No, Dong‐Joon Shin · 2007
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 les In- 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 pnif 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 Cmaxis 1+ pradicpn.