一类p元最优线性码和低相关性线性序列的构造

doi:10.3969/j.iss.0372-2012-2014.03.022

电子学报 ›› 2014, Vol. 42 ›› Issue (3): 572-577.DOI: 10.3969/j.iss.0372-2012-2014.03.022

一类p元最优线性码和低相关性线性序列的构造

唐永生^1,2, 朱士信¹, 曹德才¹, Hai Quang Dinh³

1. 合肥工业大学数学学院, 安徽合肥 230009;
2. 合肥师范学院数学系, 安徽合肥 230601;
3. 肯特州立大学数学科学系, 美国肯特州OH 44483

收稿日期:2013-04-01 修回日期:2013-06-10 出版日期:2014-03-25
- 通讯作者:
- 唐永生
- 作者简介:
- 朱士信 男，1962年7月出生于安徽枞阳县，现为合肥工业大学数学学院院长、教授、博士生导师.获国家级教学名师荣誉称号.在国内外发表学术论文100余篇.主要从事代数编码及线性和非线性移位寄存器序列的研究.E-mail：zhushixin@hfut.edu.cn
- 基金资助:
- 安徽省自然科学基金 (No.1208085MA14，No.1408085QF116）; 安徽省高校省级科学研究项目 (No.KJ2013B217，No.KJ2013B220，No.KJ2013B221）; 合肥师范学院一般研究项目 (No.2012kj10）; 国家自然科学基金 (No.61370089）

Construction of a Family of p-ary Optimal Linear Codes and Low Correlation Linear Sequences

TANG Yong-sheng^1,2, ZHU Shi-xin¹, CAO De-cai¹, Hai Quang Dinh³

1. School of Mathematics, Hefei University of Technology, Hefei, Anhui 230009, China;
2. Department of Mathematics, Hefei Normal University, Hefei, Anhui 230601, China;
3. Department of Mathematical Sciences, Kent State University, OH44483, USA

Received:2013-04-01 Revised:2013-06-10 Online:2014-03-25 Published:2014-03-25

摘要/Abstract

摘要： 在信息理论中，最优线性码具有很强的纠错能力、低相关性线性序列在密码系统和CDMA通信系统中得到了广泛应用. 因此构造最优线性码和构造低相关性线性序列具有重要的研究价值.记R=Fp+uFp，这里的p为奇素数.本文首先通过迹映射构造出环R上的一类新的线性码，然后将这类新的线性码的删余码通过Gray映射得到了域Fp上一类最优码.同时，通过迹映射构造出环R上的一类线性循环码，将这类线性循环码视为线性周期序列并通过广义Nechaev-Gray映射得到了域Fp上一类低相关线性周期序列.

关键词: 迹映射, 最优线性码, 低相关性, 线性序列

Abstract: In information theory,optimal linear codes have good capability in error-correcting in coding theory and linear sequences with low correlation have been widely used in cryptography and CDMA systems.Therefore,it has great value to study the construction of optimal linear codes and low correlation linear sequences.Let R=Fp+uFp,where p is an odd prime.A class of new linear codes over R is constructed by means of the trace map.Then a kind of optimal codes over Fp is obtained via the Gray map from the punctured new linear codes.Furthermore,a class of new linear cyclic codes over R is also constructed by means of the trace map.A kind of low correlation linear sequences over Fp is observed via the generalized Nechaev-Gray map from the class of new linear cyclic codes,which are regarded as a class of linear periodic sequences.

Key words: trace map, optimal linear codes, low correlation, linear sequences

中图分类号:

TN911.22

唐永生, 朱士信, 曹德才, Hai Quang Dinh. 一类p元最优线性码和低相关性线性序列的构造[J]. 电子学报, 2014, 42(3): 572-577.

TANG Yong-sheng, ZHU Shi-xin, CAO De-cai, Hai Quang Dinh. Construction of a Family of p-ary Optimal Linear Codes and Low Correlation Linear Sequences[J]. Acta Electronica Sinica, 2014, 42(3): 572-577.

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一类p元最优线性码和低相关性线性序列的构造

Construction of a Family of p-ary Optimal Linear Codes and Low Correlation Linear Sequences

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