几类近似达到Welch界码本的构造

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英文篇名：Constructions of some classes of codebooks nearly meeting the Welch bound 作者：张爱仙 ; 何春燕 ; 吉喆 英文作者：Zhang Aixian;He Chunyan;Ji Zhe;Department of Mathematical Sciences, Xi′an University of Technology; 关键词：码本 ; Welch界 ; 高斯和 ; 高斯周期 ; 分圆类 英文关键词：codebook;;Welch bound;;Gauss sum;;Gauss period;;cyclotomic class 中文刊名：CCSX 英文刊名：Pure and Applied Mathematics 机构：西安理工大学数学系; 出版日期：2018-09-25 出版单位：纯粹数学与应用数学 年：2018 期：v.34 基金：国家自然科学基金(11401468) 语种：中文; 页：CCSX201803012 页数：8 CN：03 ISSN：61-1240/O1 分类号：107-114

摘要

具有低相关值的码本在分频多址(CDMA)通信系统,量子信息传输,编码理论,密码等多个领域有着重要的应用.目前,最佳的码本大多是由交换群上的差集合来构造的.近年来,人们考虑构造近似最佳的码本.本文利用高斯和,高斯周期,分圆类等数论工具,构造出了三类近似达到Welch界的近似最佳码本.
        Codebooks with low correlations have important applications in code-division multiple-access(CDMA)communication systems, quantum information processing, coding theory, cryptography. Until now, most optimal codebooks are constructed by difference sets over abelian group. Recently, nearly optimal codebooks were considered. In this paper, by using the number theory such as Gauss sum, Gauss period and cyclotomic classes,we present three constructions of codebooks which are nearly meeting Welch bound.

引文

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