基于有限Zak变换的零相关区序列集构造  

Constructions of Zero Correlation Zone Sequence Sets based on Finite Zak Transform

作　　者：刘珍珍 李旭东 LIU Zhenzhen;LI Xudong(Institute of Applied Mathematics,Xihua University,Chengdu 610039,China)

机构地区：[1]西华大学理学院,四川成都610039

出　　处：《成都信息工程大学学报》2024年第3期382-388,共7页Journal of Chengdu University of Information Technology

基　　金：国家自然科学基金资助项目(62171387)。

摘　　要：针对Brodzik在2011年和2013年文中的完备序列和零相关区序列构造中参数的限制问题,分别提出完备序列和零相关区序列的新构造方法。首先,基于有限Zak变换,提出没有“参数为奇素数”限制的完备序列构造结构,并且用同余理论论证。其次,提出一种具有稀疏性、结构化特点的L×KL的零相关区序列集的Zak空间结构,从而得到零相关区序列集,用有限Zak变换和同余理论论证。相比Brodzik 2013年文中的零相关区序列集,新构造的零相关区序列集的零相关区的长度更长,序列的数量更多。In view of the restriction of parameters in the constructions of perfect sequences and zero correlation zone sequences in Brodzik’s articles published in 2011 and 2013,new construction methods of perfect sequences and zero correlation zone sequences are proposed respectively in this paper.First of all,based on the finite Zak transformation,we propose a construction of perfect sequences without the restriction that the parameter is an odd prime number,and demonstrate it with the theory of congruence.Secondly,a Zak space structure of zero correlation zone sequence sets with sparse and structured characteristics is proposedto obtain the zero correlation zone sequence sets,which are proved by the finite Zak transformation and congruence theory.Compared with the zero correlation zone sequence sets in Brodzik’s 2013 article,using the newly constructed zerocorrelation region sequence set,the length of zero correlation zone is longer and the number of sequences is more.

关 键 词：应用数学 数学与通信 有限Zak变换 完备序列 零相关区 零互相关区序列集 

分 类 号：O174[理学—数学]