{"title":"伪随机二值序列:质量度量和数论构造","authors":"Arne Winterhof","doi":"10.1587/transfun.2023sdi0001","DOIUrl":null,"url":null,"abstract":"In this survey we summarize properties of pseudorandomness and non-randomness of some number-theoretic sequences and present results on their behaviour under the following measures of pseudorandomness: balance, linear complexity, correlation measure of order $k$, expansion complexity and $2$-adic complexity. The number-theoretic sequences are the Legendre sequence and the two-prime generator, the Thue-Morse sequence and its sub-sequence along squares, and the prime omega sequences for integers and polynomials.","PeriodicalId":48822,"journal":{"name":"Ieice Transactions on Fundamentals of Electronics Communications and Computer Sciences","volume":"92 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2023-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Pseudorandom binary sequences: quality measures and number-theoretic constructions\",\"authors\":\"Arne Winterhof\",\"doi\":\"10.1587/transfun.2023sdi0001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this survey we summarize properties of pseudorandomness and non-randomness of some number-theoretic sequences and present results on their behaviour under the following measures of pseudorandomness: balance, linear complexity, correlation measure of order $k$, expansion complexity and $2$-adic complexity. The number-theoretic sequences are the Legendre sequence and the two-prime generator, the Thue-Morse sequence and its sub-sequence along squares, and the prime omega sequences for integers and polynomials.\",\"PeriodicalId\":48822,\"journal\":{\"name\":\"Ieice Transactions on Fundamentals of Electronics Communications and Computer Sciences\",\"volume\":\"92 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-05-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ieice Transactions on Fundamentals of Electronics Communications and Computer Sciences\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.1587/transfun.2023sdi0001\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Computer Science\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ieice Transactions on Fundamentals of Electronics Communications and Computer Sciences","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1587/transfun.2023sdi0001","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Computer Science","Score":null,"Total":0}
Pseudorandom binary sequences: quality measures and number-theoretic constructions
In this survey we summarize properties of pseudorandomness and non-randomness of some number-theoretic sequences and present results on their behaviour under the following measures of pseudorandomness: balance, linear complexity, correlation measure of order $k$, expansion complexity and $2$-adic complexity. The number-theoretic sequences are the Legendre sequence and the two-prime generator, the Thue-Morse sequence and its sub-sequence along squares, and the prime omega sequences for integers and polynomials.
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