一类来自函数域的伪随机序列
A class of pseudorandom sequences From Function Fields
AI总结：
本文研究了一类p-ary序列的周期、线性复杂度等特性，基于函数域构造方法，拓展了已有伪随机序列的构造。
摘要：
受Hu等人在[IEEE Trans. Inf. Theory, 53(7), 2007]中关于循环椭圆函数域上伪随机序列的构造，以及Xing等人在[IEEE Trans. Inf. Theory, 49(6), 2003]中关于从函数域构造低相关性、大线性跨度二进制序列的构造的启发，我们利用Weil在[Basic Number Theory, Grund. der Math. Wiss., Bd 144]和Deligne在[Lecture Notes in Mathematics, vol. 569 (Springer, Berlin, 1977)]中为一般代数函数域上指数和得出的界，研究了一类推广了[IEEE Trans. Inf. Theory, 49(6), 2003]和[IEEE Trans. Inf. Theory, 53(7), 2007]中构造的p-ary序列的周期、线性复杂度、线性复杂度剖面、r-模式分布、周期相关性和非线性复杂度。
英文摘要：
Motivated by the constructions of pseudorandom sequences over the cyclic elliptic function fields by Hu \textit{et al.} in \text{[IEEE Trans. Inf. Theory, 53(7), 2007]} and the constructions of low-correlation, large linear span binary sequences from function fields by Xing \textit{et al.} in \text{[IEEE Trans. Inf. Theory, 49(6), 2003]}, we utilize the bound derived by Weil \text{[Basic Number Theory, Grund. der Math. Wiss., Bd 144]} and Deligne \text{[ Lecture Notes in Mathematics, vol. 569 (Springer, Berlin, 1977)]} for the exponential sums over the general algebraic function fields and study the periods, linear complexities, linear complexity profiles, distributions of $r-$patterns, period correlation and nonlinear complexities for a class of $p-$ary sequences that generalize the constructions in \text{[IEEE Trans. Inf. Theory, 49(6), 2003]} and [IEEE Trans. Inf. Theory, 53(7), 2007].
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