{"title":"具有共同周期的二进制 m 序列的算术相关性","authors":"Xiaoyan Jing , Keqin Feng","doi":"10.1016/j.ffa.2024.102424","DOIUrl":null,"url":null,"abstract":"<div><p>The arithmetic crosscorrelation of binary <strong><em>m</em></strong>-sequences with coprime periods <span><math><msup><mrow><mn>2</mn></mrow><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msup><mo>−</mo><mn>1</mn></math></span> and <span><math><msup><mrow><mn>2</mn></mrow><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msup><mo>−</mo><mn>1</mn></math></span> (<span><math><mi>gcd</mi><mo></mo><mo>(</mo><msub><mrow><mi>n</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo><mo>=</mo><mn>1</mn></math></span>) is determined. The result shows that the absolute value of arithmetic crosscorrelation of such binary <strong><em>m</em></strong>-sequences is not greater than <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>min</mi><mo></mo><mo>(</mo><msub><mrow><mi>n</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></mrow></msup><mo>−</mo><mn>1</mn></math></span>.</p></div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":"96 ","pages":"Article 102424"},"PeriodicalIF":1.2000,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Arithmetic crosscorrelation of binary m-sequences with coprime periods\",\"authors\":\"Xiaoyan Jing , Keqin Feng\",\"doi\":\"10.1016/j.ffa.2024.102424\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The arithmetic crosscorrelation of binary <strong><em>m</em></strong>-sequences with coprime periods <span><math><msup><mrow><mn>2</mn></mrow><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msup><mo>−</mo><mn>1</mn></math></span> and <span><math><msup><mrow><mn>2</mn></mrow><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msup><mo>−</mo><mn>1</mn></math></span> (<span><math><mi>gcd</mi><mo></mo><mo>(</mo><msub><mrow><mi>n</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo><mo>=</mo><mn>1</mn></math></span>) is determined. The result shows that the absolute value of arithmetic crosscorrelation of such binary <strong><em>m</em></strong>-sequences is not greater than <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>min</mi><mo></mo><mo>(</mo><msub><mrow><mi>n</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></mrow></msup><mo>−</mo><mn>1</mn></math></span>.</p></div>\",\"PeriodicalId\":50446,\"journal\":{\"name\":\"Finite Fields and Their Applications\",\"volume\":\"96 \",\"pages\":\"Article 102424\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-04-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Finite Fields and Their Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1071579724000637\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Finite Fields and Their Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1071579724000637","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
确定了周期为 2n1-1 和 2n2-1（gcd(n1,n2)=1）的二进制 m 序列的算术相关性。结果表明，此类二进制 m 序列算术相关性的绝对值不大于 2min(n1,n2)-1。
Arithmetic crosscorrelation of binary m-sequences with coprime periods
The arithmetic crosscorrelation of binary m-sequences with coprime periods and () is determined. The result shows that the absolute value of arithmetic crosscorrelation of such binary m-sequences is not greater than .
期刊介绍：
Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering.
For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods.
The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.
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