A Family of Binary Sequences with 4-Valued Optimal Out-of-Phase Correlation and Large Linear Span

Xiangyong ZENG  Lei HU  Wenfeng JIANG  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A   No.7   pp.2029-2035
Publication Date: 2006/07/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.7.2029
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Information Theory
Keyword: 
sequence,  4-valued correlation,  linear span,  ideal autocorrelation,  

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Summary: 
In this paper, a new family S(r) of 2n binary sequences of period 2n-1 is proposed, where n ≡ 2 mod 4 and gcd(r, 2n/2-1)=1. The presented family takes 4-valued out-of-phase auto- and cross-correlation values -1, 2n/2-1, and 2n/2+1-1, and its correlation distribution is determined. For r=2(n-2)/4-1, each sequence in S(r), except the unique ideal autocorrelation sequence in the family, is proved to have a large linear span n2n/2-2, whilst the linear span of the latter is n2(n-2)/4-1.