{"title":"Construction of spectrally-null-constrained zero-correlation zone sequences with flexible support","authors":"Nishant Kumar, Palash Sarkar, Sudhan Majhi","doi":"10.1007/s12095-024-00715-0","DOIUrl":null,"url":null,"abstract":"<p>In recent years, zero-correlation zone (ZCZ) sequences have been studied due to their significant applications in quasi-synchronous code division multiple access (QS-CDMA) systems and other wireless communication domains. However, in a cognitive radio (CR) network, it is desirable to design ZCZ sequences having spectrally-null-constrained (SNC) property to achieve a low spectral density profile. This paper focuses on the construction of SNC-ZCZ sequences having flexible support, where support refers to a collection of indices corresponding to non-zero entries in the sequence. The proposed SNC-ZCZ sequences are reduced to traditional ZCZ sequences when the support size is equal to the length of the sequence. To obtain ZCZ sequences, we first propose a construction of traditional/SNC-complete complementary codes (SNC-CCCs) using a class of extended Boolean functions (EBFs). With the help of this class, we propose another class of EBFs that generates asymptotically optimal traditional/SNC-ZCZ sequences of prime-power lengths with respect to Tang-Fan-Matsufuzi bound. Furthermore, a relation between the second-order cosets of first-order generalized Reed-Muller (GRM) code and the proposed traditional ZCZ sequences is also established. The enumeration of traditional ZCZ sequences within a GRM code is also established. This enumeration is achieved by tallying the distinct second-order cosets of the first-order GRM code and quantifying the number of ZCZ sequences residing within a particular coset. Moreover, the Hamming distance of the proposed traditional ZCZ sequences is also computed.</p>","PeriodicalId":10788,"journal":{"name":"Cryptography and Communications","volume":"31 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Cryptography and Communications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s12095-024-00715-0","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In recent years, zero-correlation zone (ZCZ) sequences have been studied due to their significant applications in quasi-synchronous code division multiple access (QS-CDMA) systems and other wireless communication domains. However, in a cognitive radio (CR) network, it is desirable to design ZCZ sequences having spectrally-null-constrained (SNC) property to achieve a low spectral density profile. This paper focuses on the construction of SNC-ZCZ sequences having flexible support, where support refers to a collection of indices corresponding to non-zero entries in the sequence. The proposed SNC-ZCZ sequences are reduced to traditional ZCZ sequences when the support size is equal to the length of the sequence. To obtain ZCZ sequences, we first propose a construction of traditional/SNC-complete complementary codes (SNC-CCCs) using a class of extended Boolean functions (EBFs). With the help of this class, we propose another class of EBFs that generates asymptotically optimal traditional/SNC-ZCZ sequences of prime-power lengths with respect to Tang-Fan-Matsufuzi bound. Furthermore, a relation between the second-order cosets of first-order generalized Reed-Muller (GRM) code and the proposed traditional ZCZ sequences is also established. The enumeration of traditional ZCZ sequences within a GRM code is also established. This enumeration is achieved by tallying the distinct second-order cosets of the first-order GRM code and quantifying the number of ZCZ sequences residing within a particular coset. Moreover, the Hamming distance of the proposed traditional ZCZ sequences is also computed.