{"title":"任意大小字母上广义Rudin-Shapiro序列的2阶离散相关","authors":"Pierre-Adrien Tahay","doi":"10.2478/udt-2020-0001","DOIUrl":null,"url":null,"abstract":"Abstract In 2009, Grant, Shallit, and Stoll [Acta Arith. 140 (2009), [345–368] constructed a large family of pseudorandom sequences, called generalized Rudin--Shapiro sequences, for which they established some results about the average of discrete correlation coefficients of order 2 in cases where the size of the alphabet is a prime number or a squarefree product of primes. We establish similar results for an even larger family of pseudorandom sequences, constructed via difference matrices, in the case of an alphabet of any size. The constructions generalize those from Grant et al. In the case where the size of the alphabet is squarefree and where there are at least two prime factors, we obtain an improvement in the error term by comparison with the result of Grant et al.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"33 1","pages":"1 - 26"},"PeriodicalIF":0.0000,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Discrete Correlation of Order 2 of Generalized Rudin-Shapiro Sequences on Alphabets of Arbitrary Size\",\"authors\":\"Pierre-Adrien Tahay\",\"doi\":\"10.2478/udt-2020-0001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In 2009, Grant, Shallit, and Stoll [Acta Arith. 140 (2009), [345–368] constructed a large family of pseudorandom sequences, called generalized Rudin--Shapiro sequences, for which they established some results about the average of discrete correlation coefficients of order 2 in cases where the size of the alphabet is a prime number or a squarefree product of primes. We establish similar results for an even larger family of pseudorandom sequences, constructed via difference matrices, in the case of an alphabet of any size. The constructions generalize those from Grant et al. In the case where the size of the alphabet is squarefree and where there are at least two prime factors, we obtain an improvement in the error term by comparison with the result of Grant et al.\",\"PeriodicalId\":23390,\"journal\":{\"name\":\"Uniform distribution theory\",\"volume\":\"33 1\",\"pages\":\"1 - 26\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-02-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Uniform distribution theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2478/udt-2020-0001\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Uniform distribution theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/udt-2020-0001","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
摘要
2009年,Grant, Shallit, and Stoll [Acta Arith. 140(2009),[345-368]构造了一大族伪随机序列,称为广义Rudin—Shapiro序列,在字母表大小为素数或素数的无平方积的情况下,他们建立了关于2阶离散相关系数平均值的一些结果。我们建立了类似的结果,甚至更大的伪随机序列家族,通过差分矩阵构造,在任何大小的字母表的情况下。这些结构概括了Grant等人的结构。在字母表的大小是无平方的并且至少有两个素数因子的情况下,与Grant等人的结果相比,我们获得了误差项的改进。
Discrete Correlation of Order 2 of Generalized Rudin-Shapiro Sequences on Alphabets of Arbitrary Size
Abstract In 2009, Grant, Shallit, and Stoll [Acta Arith. 140 (2009), [345–368] constructed a large family of pseudorandom sequences, called generalized Rudin--Shapiro sequences, for which they established some results about the average of discrete correlation coefficients of order 2 in cases where the size of the alphabet is a prime number or a squarefree product of primes. We establish similar results for an even larger family of pseudorandom sequences, constructed via difference matrices, in the case of an alphabet of any size. The constructions generalize those from Grant et al. In the case where the size of the alphabet is squarefree and where there are at least two prime factors, we obtain an improvement in the error term by comparison with the result of Grant et al.