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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 *Tr*_{1}^{m}[*Tr*_{m}^{n}(α^{bt}+γ_{i}α^{dt})]^{r} for generating *p*-ary sequences of period *p*^{n}-1, where *n*=2*m*, *d*=*up*^{m}*v*, *b*=*u**v*, γ_{i} *p*^{n}), and *p* is an arbitrary prime number, several methods to choose the parameter *d* are provided. The obtained sequences with family size *p*^{n} are of four-valued, five-valued, six-valued or seven-valued correlation and the maximum nontrivial correlation value is (*u*+*v*-1)*p*^{m}-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].

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E91-A No.8 pp.2263-2268

- Publication Date
- 2008/08/01

- Publicized

- Online ISSN
- 1745-1337

- DOI
- 10.1093/ietfec/e91-a.8.2263

- Type of Manuscript
- LETTER

- Category
- Information Theory

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Fanxin ZENG, Zhenyu ZHANG, "Several Families of Sequences with Low Correlation and Large Linear Span" in IEICE TRANSACTIONS on Fundamentals,
vol. E91-A, no. 8, pp. 2263-2268, August 2008, doi: 10.1093/ietfec/e91-a.8.2263.

Abstract: 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 *Tr*_{1}^{m}[*Tr*_{m}^{n}(α^{bt}+γ_{i}α^{dt})]^{r} for generating *p*-ary sequences of period *p*^{n}-1, where *n*=2*m*, *d*=*up*^{m}*v*, *b*=*u**v*, γ_{i} *p*^{n}), and *p* is an arbitrary prime number, several methods to choose the parameter *d* are provided. The obtained sequences with family size *p*^{n} are of four-valued, five-valued, six-valued or seven-valued correlation and the maximum nontrivial correlation value is (*u*+*v*-1)*p*^{m}-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].

URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e91-a.8.2263/_p

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@ARTICLE{e91-a_8_2263,

author={Fanxin ZENG, Zhenyu ZHANG, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Several Families of Sequences with Low Correlation and Large Linear Span},

year={2008},

volume={E91-A},

number={8},

pages={2263-2268},

abstract={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 *Tr*_{1}^{m}[*Tr*_{m}^{n}(α^{bt}+γ_{i}α^{dt})]^{r} for generating *p*-ary sequences of period *p*^{n}-1, where *n*=2*m*, *d*=*up*^{m}*v*, *b*=*u**v*, γ_{i} *p*^{n}), and *p* is an arbitrary prime number, several methods to choose the parameter *d* are provided. The obtained sequences with family size *p*^{n} are of four-valued, five-valued, six-valued or seven-valued correlation and the maximum nontrivial correlation value is (*u*+*v*-1)*p*^{m}-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].

keywords={},

doi={10.1093/ietfec/e91-a.8.2263},

ISSN={1745-1337},

month={August},}

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TY - JOUR

TI - Several Families of Sequences with Low Correlation and Large Linear Span

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 2263

EP - 2268

AU - Fanxin ZENG

AU - Zhenyu ZHANG

PY - 2008

DO - 10.1093/ietfec/e91-a.8.2263

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E91-A

IS - 8

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - August 2008

AB - 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 *Tr*_{1}^{m}[*Tr*_{m}^{n}(α^{bt}+γ_{i}α^{dt})]^{r} for generating *p*-ary sequences of period *p*^{n}-1, where *n*=2*m*, *d*=*up*^{m}*v*, *b*=*u**v*, γ_{i} *p*^{n}), and *p* is an arbitrary prime number, several methods to choose the parameter *d* are provided. The obtained sequences with family size *p*^{n} are of four-valued, five-valued, six-valued or seven-valued correlation and the maximum nontrivial correlation value is (*u*+*v*-1)*p*^{m}-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].

ER -