Cross-Correlation Distribution of p-Ary m-Sequence and Its p + 1 Decimated Sequences with Shorter Period

Eun-Young SEO  Young-Sik KIM  Jong-Seon NO  Dong-Joon SHIN  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E90-A   No.11   pp.2568-2574
Publication Date: 2007/11/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e90-a.11.2568
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Spread Spectrum Technologies and Applications
Keyword: 
cross-correlation,  p-ary m-sequences,  sequences,  

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Summary: 
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 = 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 because gcd(d, pn - 1) = p + 1. The maximum magnitude of their cross-correlation values is 1 + p if l ≡ 0 mod p + 1 for n ≡ 0 mod 4 or l ≡ (p + 1)/2 mod p + 1 for n ≡ 2 mod 4 and otherwise, 1 + . 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.