On the Linear Span of a Binary Sequence Family with Optimal Correlation Properties

Xiangyong ZENG  John Q. LIU  Lei HU  Desmond P. TAYLOR  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A   No.2   pp.664-672
Publication Date: 2008/02/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.2.664
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Information Theory
Sequences,  optimal correlation,  linear span,  ideal autocorrelation,  

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A new subfamily of sequences with optimal correlation properties is constructed for the generalized Kasami set. A lower bound on the linear span is established. It is proved that with suitable choices of parameters, this subfamily has exponentially larger linear spans than either No sequences or TN sequences. A class of sequences with ideal autocorrelation is also proved to have large linear span.