一类四值相关的p元序列的研究

数学物理学报 ›› 2011, Vol. 31 ›› Issue (3): 620-627.

一类四值相关的p元序列的研究

李念, 李胜华*

湖北大学数学与计算机科学学院武汉 430062

收稿日期:2008-12-27 修回日期:2010-06-11 出版日期:2011-06-25 发布日期:2011-06-25
通讯作者: 李胜华 E-mail:linian89700142@yahoo.com.cn; lsh@hubu.edu.cn
基金资助:
湖北省自然科学基金重点项目(2009CDA147)、湖北省教育厅优秀中青年人才项目(Q20101004)和应用数学湖北省重点实验室开放课题(O24017)资助

Study on a Class of p-ary Sequences with Four-valued Crosscorrelation

LI Nian, LI Sheng-Hua*

Faculty of Mathematics and Computer Science, Hubei University, Wuhan 430062

Received:2008-12-27 Revised:2010-06-11 Online:2011-06-25 Published:2011-06-25
Contact: LI Sheng-Hua E-mail:linian89700142@yahoo.com.cn; lsh@hubu.edu.cn
Supported by:
湖北省自然科学基金重点项目(2009CDA147)、湖北省教育厅优秀中青年人才项目(Q20101004)和应用数学湖北省重点实验室开放课题(O24017)资助

摘要/Abstract

摘要：

对于奇数n>0, 素数p≡ 3 (mod, 4), 设α是有限域F_pⁿ的一个本原元, d = pⁿ-1/2 + p^k且0 ≤ k < n. 该文证明了一类p元序列u(t) =Tr(aα^dt), a ∈F*_pⁿ与m序列v(t)=Tr(α^t)是四值相关的, 且它们的相关值分布也被完全确定.

关键词: 有限域, m序列, Walsh变换, 互相关性

Abstract:

For an odd integer n > 0 and a prime p≡ 3 (mod 4), let be a primitive element of F_pⁿ , where d = pⁿ-1/2 + p^k and 0 ≤ k < n. The crosscorrelation of p-ary sequences u(t) =Tr(aα^dt), a ∈F*_pⁿ, and m sequences v(t) = Tr(α^t) is proved to be four-valued. Moreover, the distribution is also completely determined.

Key words: Finite field, m sequence, Walsh transform, Crosscorrelation

中图分类号:

94A55

李念, 李胜华. 一类四值相关的p元序列的研究[J]. 数学物理学报, 2011, 31(3): 620-627.

LI Nian, LI Sheng-Hua. Study on a Class of p-ary Sequences with Four-valued Crosscorrelation[J]. Acta mathematica scientia,Series A, 2011, 31(3): 620-627.

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