{"title":"在F2+uF2上构造DNA编码的双循环码。","authors":"Arunothai Kanlaya, Chakkrid Klin-Eam","doi":"10.1089/cmb.2022.0151","DOIUrl":null,"url":null,"abstract":"<p><p>In this article, we investigate the algebraic structure of double cyclic codes of length <math><mrow><mo>(</mo><mrow><mi>α</mi><mo>,</mo><mi>β</mi></mrow><mo>)</mo></mrow></math> over <math><msub><mrow><mstyle><mi>F</mi></mstyle></mrow><mrow><mn>2</mn></mrow></msub><mo>+</mo><mi>u</mi><msub><mrow><mstyle><mi>F</mi></mstyle></mrow><mrow><mn>2</mn></mrow></msub></math> with <math><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>0</mn></math> and construct DNA codes from these codes. The theory of constructing double cyclic codes suitable for DNA codes is studied. We provide the necessary and sufficient conditions for the double cyclic codes to be reversible and reversible-complement codes. As an illustration, we present some of the DNA codes generated from our results.</p>","PeriodicalId":15526,"journal":{"name":"Journal of Computational Biology","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"<ArticleTitle xmlns:ns0=\\\"http://www.w3.org/1998/Math/MathML\\\">Constructing Double Cyclic Codes over <ns0:math><ns0:msub><ns0:mrow><ns0:mstyle><ns0:mi>F</ns0:mi></ns0:mstyle></ns0:mrow><ns0:mrow><ns0:mn>2</ns0:mn></ns0:mrow></ns0:msub><ns0:mo>+</ns0:mo><ns0:mi>u</ns0:mi><ns0:msub><ns0:mrow><ns0:mstyle><ns0:mi>F</ns0:mi></ns0:mstyle></ns0:mrow><ns0:mrow><ns0:mn>2</ns0:mn></ns0:mrow></ns0:msub></ns0:math> for DNA Codes.\",\"authors\":\"Arunothai Kanlaya, Chakkrid Klin-Eam\",\"doi\":\"10.1089/cmb.2022.0151\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>In this article, we investigate the algebraic structure of double cyclic codes of length <math><mrow><mo>(</mo><mrow><mi>α</mi><mo>,</mo><mi>β</mi></mrow><mo>)</mo></mrow></math> over <math><msub><mrow><mstyle><mi>F</mi></mstyle></mrow><mrow><mn>2</mn></mrow></msub><mo>+</mo><mi>u</mi><msub><mrow><mstyle><mi>F</mi></mstyle></mrow><mrow><mn>2</mn></mrow></msub></math> with <math><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>0</mn></math> and construct DNA codes from these codes. The theory of constructing double cyclic codes suitable for DNA codes is studied. We provide the necessary and sufficient conditions for the double cyclic codes to be reversible and reversible-complement codes. As an illustration, we present some of the DNA codes generated from our results.</p>\",\"PeriodicalId\":15526,\"journal\":{\"name\":\"Journal of Computational Biology\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2023-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Computational Biology\",\"FirstCategoryId\":\"99\",\"ListUrlMain\":\"https://doi.org/10.1089/cmb.2022.0151\",\"RegionNum\":4,\"RegionCategory\":\"生物学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"BIOCHEMICAL RESEARCH METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational Biology","FirstCategoryId":"99","ListUrlMain":"https://doi.org/10.1089/cmb.2022.0151","RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"BIOCHEMICAL RESEARCH METHODS","Score":null,"Total":0}
Constructing Double Cyclic Codes over F2+uF2 for DNA Codes.
In this article, we investigate the algebraic structure of double cyclic codes of length over with and construct DNA codes from these codes. The theory of constructing double cyclic codes suitable for DNA codes is studied. We provide the necessary and sufficient conditions for the double cyclic codes to be reversible and reversible-complement codes. As an illustration, we present some of the DNA codes generated from our results.
期刊介绍：
Journal of Computational Biology is the leading peer-reviewed journal in computational biology and bioinformatics, publishing in-depth statistical, mathematical, and computational analysis of methods, as well as their practical impact. Available only online, this is an essential journal for scientists and students who want to keep abreast of developments in bioinformatics.
Journal of Computational Biology coverage includes:
-Genomics
-Mathematical modeling and simulation
-Distributed and parallel biological computing
-Designing biological databases
-Pattern matching and pattern detection
-Linking disparate databases and data
-New tools for computational biology
-Relational and object-oriented database technology for bioinformatics
-Biological expert system design and use
-Reasoning by analogy, hypothesis formation, and testing by machine
-Management of biological databases
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