Abbas Alhakim, Chris J. Mitchell, Janusz Szmidt, Peter R. Wild
{"title":"非二进制字母上的可定向序列","authors":"Abbas Alhakim, Chris J. Mitchell, Janusz Szmidt, Peter R. Wild","doi":"10.1007/s12095-024-00742-x","DOIUrl":null,"url":null,"abstract":"<p>We describe new, simple, recursive methods of construction for <i>orientable sequences</i> over an arbitrary finite alphabet, i.e. periodic sequences in which any sub-sequence of <i>n</i> consecutive elements occurs at most once in a period in either direction. In particular we establish how two variants of a generalised Lempel homomorphism can be used to recursively construct such sequences, generalising previous work on the binary case. We also derive an upper bound on the period of an orientable sequence.</p>","PeriodicalId":10788,"journal":{"name":"Cryptography and Communications","volume":"42 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Orientable sequences over non-binary alphabets\",\"authors\":\"Abbas Alhakim, Chris J. Mitchell, Janusz Szmidt, Peter R. Wild\",\"doi\":\"10.1007/s12095-024-00742-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We describe new, simple, recursive methods of construction for <i>orientable sequences</i> over an arbitrary finite alphabet, i.e. periodic sequences in which any sub-sequence of <i>n</i> consecutive elements occurs at most once in a period in either direction. In particular we establish how two variants of a generalised Lempel homomorphism can be used to recursively construct such sequences, generalising previous work on the binary case. We also derive an upper bound on the period of an orientable sequence.</p>\",\"PeriodicalId\":10788,\"journal\":{\"name\":\"Cryptography and Communications\",\"volume\":\"42 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-02\",\"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/s12095-024-00742-x\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Cryptography and Communications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s12095-024-00742-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We describe new, simple, recursive methods of construction for orientable sequences over an arbitrary finite alphabet, i.e. periodic sequences in which any sub-sequence of n consecutive elements occurs at most once in a period in either direction. In particular we establish how two variants of a generalised Lempel homomorphism can be used to recursively construct such sequences, generalising previous work on the binary case. We also derive an upper bound on the period of an orientable sequence.