Several Families of Sequences with Low Correlation and Large Linear Span

Fanxin ZENG  Zhenyu ZHANG  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A   No.8   pp.2263-2268
Publication Date: 2008/08/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.8.2263
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Information Theory
sequence,  low correlation,  linear span,  Niho-type decimation,  DS-CDMA/UWB,  

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In DS-CDMA systems and DS-UWB radios, low correlation of spreading sequences can greatly help to minimize multiple access interference (MAI) and large linear span of spreading sequences can reduce their predictability. In this letter, new sequence sets with low correlation and large linear span are proposed. Based on the construction Tr1m[Trmnbtiαdt)]r for generating p-ary sequences of period pn-1, where n=2m, d=upm v, b=u v, γi GF(pn), and p is an arbitrary prime number, several methods to choose the parameter d are provided. The obtained sequences with family size pn are of four-valued, five-valued, six-valued or seven-valued correlation and the maximum nontrivial correlation value is (u+v-1)pm-1. The simulation by a computer shows that the linear span of the new sequences is larger than that of the sequences with Niho-type and Welch-type decimations, and similar to that of [10].