{"title":"Three new classes of spreading sequence sets with low correlation and PAPR","authors":"Can Xiang , Chunming Tang , Wenwei Qiu","doi":"10.1016/j.ffa.2025.102575","DOIUrl":null,"url":null,"abstract":"<div><div>Spreading sequences have recently received a lot of attention, as some of these sequences are used to design spreading sequence sets with low correlation and low peak-to-average power ratio (PAPR for short) and which have very important applications in communication systems. It was recently reported that a small amount of work on constructing binary spreading sequence sets with low correlation and low PAPR has been done. However, till now only one work on constructing <em>p</em>-ary spreading sequence sets with low correlation and low PAPR for odd prime <em>p</em> has been done by using special functions in Liu et al. (2023) <span><span>[11]</span></span>, and it is, in general, hard to design spreading sequence sets with low correlation and low PAPR. In this paper, we investigate this idea further by using some quadratic functions over finite fields, thereby obtain three classes of <em>p</em>-ary spreading sequence sets, and explicitly determine their parameters. The parameters of these <em>p</em>-ary spreading sequence sets are new and flexible. Furthermore, the results of this paper show that these obtained <em>p</em>-ary spreading sequence sets have low correlation and PAPR.</div></div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":"103 ","pages":"Article 102575"},"PeriodicalIF":1.2000,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Finite Fields and Their Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S107157972500005X","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/1/22 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Spreading sequences have recently received a lot of attention, as some of these sequences are used to design spreading sequence sets with low correlation and low peak-to-average power ratio (PAPR for short) and which have very important applications in communication systems. It was recently reported that a small amount of work on constructing binary spreading sequence sets with low correlation and low PAPR has been done. However, till now only one work on constructing p-ary spreading sequence sets with low correlation and low PAPR for odd prime p has been done by using special functions in Liu et al. (2023) [11], and it is, in general, hard to design spreading sequence sets with low correlation and low PAPR. In this paper, we investigate this idea further by using some quadratic functions over finite fields, thereby obtain three classes of p-ary spreading sequence sets, and explicitly determine their parameters. The parameters of these p-ary spreading sequence sets are new and flexible. Furthermore, the results of this paper show that these obtained p-ary spreading sequence sets have low correlation and PAPR.
扩频序列近年来受到广泛关注，其中一些序列用于设计低相关和低峰均功率比（PAPR）的扩频序列集，在通信系统中有着非常重要的应用。近年来，在构造低相关、低PAPR的二值扩展序列集方面做了少量的工作。然而，迄今为止只有Liu et al.(2023)[11]利用特殊函数构造奇素数p的低相关、低PAPR的p元扩展序列集，一般来说，设计低相关、低PAPR的扩展序列集是比较困难的。本文利用有限域上的二次函数进一步研究了这一思想，得到了三类p元扩展序列集，并显式地确定了它们的参数。这些p元扩展序列集的参数是新的和灵活的。此外，本文的结果表明，这些p元扩展序列集具有较低的相关性和PAPR。
期刊介绍：
Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering.
For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods.
The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
