English

A class of pseudorandom sequences From Function Fields

Information Theory 2026-02-09 v2 math.IT

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 rr-patterns, period correlation and nonlinear complexities for a class of pp-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}
}
R2 v1 2026-07-01T09:30:05.909Z