New Families of Binary Sequences with Low Correlation and Large Size

Zhengchun ZHOU  Xiaohu TANG  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E92-A    No.1    pp.291-297
Publication Date: 2009/01/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E92.A.291
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Coding Theory
Keyword: 
binary sequence,  periodic correlation,  low correlation,  large family size,  linear span,  quadratic form,  

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Summary: 
In this paper, for odd n and any k with gcd(n,k) = 1, new binary sequence families Sk of period 2n-1 are constructed. These families have maximum correlation , family size 22n+2n+1 and maximum linear span . The correlation distribution of Sk is completely determined as well. Compared with the modified Gold codes with the same family size, the proposed families have the same period and correlation properties, but larger linear span. As good candidates with low correlation and large family size, the new families contain the Gold sequences and the Gold-like sequences. Furthermore, Sk includes a subfamily which has the same period, correlation distribution, family size and linear span as the family So(2) recently constructed by Yu and Gong. In particular, when k=1, is exactly So(2).