论文标题
在任意大小的字母上的广义rudin--shapiro序列的第2阶的离散相关性
Discrete correlation of order 2 of generalized Rudin--Shapiro sequences on alphabets of arbitrary size
论文作者
论文摘要
在2009年，格兰特，志愿和斯托尔构建了一个庞大的伪序列序列，称为广义rudin--shapiro序列，为此，在字母表的大小为质量数量或无平方量的数量的平均值的情况下，他们建立了一些关于订单2的平均订单相关系数的结果。在任何大小的字母的情况下，我们为通过差异矩阵构建的较大的假序列序列建立了相似的结果。这些结构概括了Grant等人。如果字母的大小是无方形的，并且至少有两个主要因素，则通过与Grant等人的结果相比，我们获得了误差项的改善。
In 2009, Grant, Shallit, and Stoll 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.
