{"title":"基于扩展布尔函数的渐近最优非周期性准互补序列集","authors":"Bingsheng Shen, Tao Yu, Zhengchun Zhou, Yang Yang","doi":"10.1007/s10623-024-01501-y","DOIUrl":null,"url":null,"abstract":"<p>Quasi-complementary sequence sets (QCSSs) are important in modern communication systems as they are capable of supporting more users, which is desired in applications like MC-CDMA nowadays. Although several constructions of aperiodic QCSSs have been proposed in the literature, the known optimal aperiodic QCSSs have limited length or have large alphabet. In this paper, based on extended Boolean functions, we present two constructions of aperiodic QCSSs with parameters <span>\\((q(p_0-1),q,q-t,q)\\)</span> and <span>\\((q^m(p_0-1),q^m,q^m-t,q^m)\\)</span>, where <span>\\(q\\ge 3\\)</span> is an odd integer, <span>\\(p_0\\)</span> is the minimum prime factor of <i>q</i>. The proposed constructions can generate asymptotically optimal or near-optimal aperiodic QCSSs with new parameters.\n</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"53 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Asymptotically optimal aperiodic quasi-complementary sequence sets based on extended Boolean functions\",\"authors\":\"Bingsheng Shen, Tao Yu, Zhengchun Zhou, Yang Yang\",\"doi\":\"10.1007/s10623-024-01501-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Quasi-complementary sequence sets (QCSSs) are important in modern communication systems as they are capable of supporting more users, which is desired in applications like MC-CDMA nowadays. Although several constructions of aperiodic QCSSs have been proposed in the literature, the known optimal aperiodic QCSSs have limited length or have large alphabet. In this paper, based on extended Boolean functions, we present two constructions of aperiodic QCSSs with parameters <span>\\\\((q(p_0-1),q,q-t,q)\\\\)</span> and <span>\\\\((q^m(p_0-1),q^m,q^m-t,q^m)\\\\)</span>, where <span>\\\\(q\\\\ge 3\\\\)</span> is an odd integer, <span>\\\\(p_0\\\\)</span> is the minimum prime factor of <i>q</i>. The proposed constructions can generate asymptotically optimal or near-optimal aperiodic QCSSs with new parameters.\\n</p>\",\"PeriodicalId\":11130,\"journal\":{\"name\":\"Designs, Codes and Cryptography\",\"volume\":\"53 1\",\"pages\":\"\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-09-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Designs, Codes and Cryptography\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10623-024-01501-y\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Designs, Codes and Cryptography","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10623-024-01501-y","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
Asymptotically optimal aperiodic quasi-complementary sequence sets based on extended Boolean functions
Quasi-complementary sequence sets (QCSSs) are important in modern communication systems as they are capable of supporting more users, which is desired in applications like MC-CDMA nowadays. Although several constructions of aperiodic QCSSs have been proposed in the literature, the known optimal aperiodic QCSSs have limited length or have large alphabet. In this paper, based on extended Boolean functions, we present two constructions of aperiodic QCSSs with parameters \((q(p_0-1),q,q-t,q)\) and \((q^m(p_0-1),q^m,q^m-t,q^m)\), where \(q\ge 3\) is an odd integer, \(p_0\) is the minimum prime factor of q. The proposed constructions can generate asymptotically optimal or near-optimal aperiodic QCSSs with new parameters.
期刊介绍：
Designs, Codes and Cryptography is an archival peer-reviewed technical journal publishing original research papers in the designated areas. There is a great deal of activity in design theory, coding theory and cryptography, including a substantial amount of research which brings together more than one of the subjects. While many journals exist for each of the individual areas, few encourage the interaction of the disciplines.
The journal was founded to meet the needs of mathematicians, engineers and computer scientists working in these areas, whose interests extend beyond the bounds of any one of the individual disciplines. The journal provides a forum for high quality research in its three areas, with papers touching more than one of the areas especially welcome.
The journal also considers high quality submissions in the closely related areas of finite fields and finite geometries, which provide important tools for both the construction and the actual application of designs, codes and cryptographic systems. In particular, it includes (mostly theoretical) papers on computational aspects of finite fields. It also considers topics in sequence design, which frequently admit equivalent formulations in the journal’s main areas.
Designs, Codes and Cryptography is mathematically oriented, emphasizing the algebraic and geometric aspects of the areas it covers. The journal considers high quality papers of both a theoretical and a practical nature, provided they contain a substantial amount of mathematics.
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