{"title":"来自广义 GMW 序列对的唐-龚交错序列的对称 2-adic 复杂性","authors":"Bo Yang, Kangkang He, Xiangyong Zeng, Zibi Xiao","doi":"10.1007/s10623-024-01399-6","DOIUrl":null,"url":null,"abstract":"<p>Tang–Gong interleaved sequences constructed from the generalized GMW sequence pair are a class of binary sequences with optimal autocorrelation magnitude. In this paper, the symmetric 2-adic complexity of these sequences is investigated. We first derive a lower bound on their 2-adic complexity by extending the method proposed by Hu. Then, by analysing the algebraic structure of these sequences, a lower bound on their symmetric 2-adic complexity is obtained. Our result shows that the symmetric 2-adic complexity of these sequences is large enough to resist attacks with the rational approximation algorithm.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Symmetric 2-adic complexity of Tang–Gong interleaved sequences from generalized GMW sequence pair\",\"authors\":\"Bo Yang, Kangkang He, Xiangyong Zeng, Zibi Xiao\",\"doi\":\"10.1007/s10623-024-01399-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Tang–Gong interleaved sequences constructed from the generalized GMW sequence pair are a class of binary sequences with optimal autocorrelation magnitude. In this paper, the symmetric 2-adic complexity of these sequences is investigated. We first derive a lower bound on their 2-adic complexity by extending the method proposed by Hu. Then, by analysing the algebraic structure of these sequences, a lower bound on their symmetric 2-adic complexity is obtained. Our result shows that the symmetric 2-adic complexity of these sequences is large enough to resist attacks with the rational approximation algorithm.</p>\",\"PeriodicalId\":11130,\"journal\":{\"name\":\"Designs, Codes and Cryptography\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-04-16\",\"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/s10623-024-01399-6\",\"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/s10623-024-01399-6","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}
Symmetric 2-adic complexity of Tang–Gong interleaved sequences from generalized GMW sequence pair
Tang–Gong interleaved sequences constructed from the generalized GMW sequence pair are a class of binary sequences with optimal autocorrelation magnitude. In this paper, the symmetric 2-adic complexity of these sequences is investigated. We first derive a lower bound on their 2-adic complexity by extending the method proposed by Hu. Then, by analysing the algebraic structure of these sequences, a lower bound on their symmetric 2-adic complexity is obtained. Our result shows that the symmetric 2-adic complexity of these sequences is large enough to resist attacks with the rational approximation algorithm.
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.