A class of pseudorandom sequences From Function Fields
Abstract
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 patterns, period correlation and nonlinear complexities for a class of ary sequences that generalize the constructions in \text{[IEEE Trans. Inf. Theory, 49(6), 2003]} and [IEEE Trans. Inf. Theory, 53(7), 2007].
Keywords
Cite
@article{arxiv.2602.01154,
title = {A class of pseudorandom sequences From Function Fields},
author = {Xiaofeng Liu and Jun Zhang and Fang-Wei Fu},
journal= {arXiv preprint arXiv:2602.01154},
year = {2026}
}