{"title":"通过差集对的二进制序列/数组对：一种递归方法","authors":"K. Arasu, Anika Goyal, Abhishek Puri","doi":"10.22108/TOC.2017.21466","DOIUrl":null,"url":null,"abstract":"Binary array pairs with optimal/ideal correlation values and their algebraic counterparts textquotedblleft difference set pairstextquotedblright;(DSPs) in abelian groups are studied. In addition to generalizing known 1-dimensional (sequences) examples, we provide four new recursive constructions, unifying previously obtained ones. Any further advancements in the construction of binary sequences/arrays with optimal/ideal correlation values (equivalently cyclic/abelian difference sets) would give rise to richer classes of DSPs (and hence binary perfect array pairs). Discrete signals arising from DSPs find applications in cryptography, CDMA systems, radar and wireless communications.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"6 1","pages":"19-36"},"PeriodicalIF":0.6000,"publicationDate":"2017-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Binary sequence/array pairs via diference set pairs: A recursive approach\",\"authors\":\"K. Arasu, Anika Goyal, Abhishek Puri\",\"doi\":\"10.22108/TOC.2017.21466\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Binary array pairs with optimal/ideal correlation values and their algebraic counterparts textquotedblleft difference set pairstextquotedblright;(DSPs) in abelian groups are studied. In addition to generalizing known 1-dimensional (sequences) examples, we provide four new recursive constructions, unifying previously obtained ones. Any further advancements in the construction of binary sequences/arrays with optimal/ideal correlation values (equivalently cyclic/abelian difference sets) would give rise to richer classes of DSPs (and hence binary perfect array pairs). Discrete signals arising from DSPs find applications in cryptography, CDMA systems, radar and wireless communications.\",\"PeriodicalId\":43837,\"journal\":{\"name\":\"Transactions on Combinatorics\",\"volume\":\"6 1\",\"pages\":\"19-36\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2017-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions on Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22108/TOC.2017.21466\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions on Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22108/TOC.2017.21466","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Binary sequence/array pairs via diference set pairs: A recursive approach
Binary array pairs with optimal/ideal correlation values and their algebraic counterparts textquotedblleft difference set pairstextquotedblright;(DSPs) in abelian groups are studied. In addition to generalizing known 1-dimensional (sequences) examples, we provide four new recursive constructions, unifying previously obtained ones. Any further advancements in the construction of binary sequences/arrays with optimal/ideal correlation values (equivalently cyclic/abelian difference sets) would give rise to richer classes of DSPs (and hence binary perfect array pairs). Discrete signals arising from DSPs find applications in cryptography, CDMA systems, radar and wireless communications.
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