Manfred Madritsch ; Robert Tichy - On Finite Pseudorandom Binary Sequences: Generalized polynomials

hrj:17905 - Hardy-Ramanujan Journal, April 27, 2026, Volume 48 - 2025 - https://doi.org/10.46298/hrj.2026.17905
On Finite Pseudorandom Binary Sequences: Generalized polynomialsArticle

Authors: Manfred Madritsch ; Robert Tichy 1


In the present paper we generate binary pseudorandom sequences using generalized polynomials. A generalized polynomial is a function in whose description we not only allow addition and product (as it is the case in usual polynomials) but also the floor function. We estimate the well-distribution measure, looking at the "randomness" along arithmetic progressions.


Volume: Volume 48 - 2025
Published on: April 27, 2026
Accepted on: April 27, 2026
Submitted on: April 3, 2026
Keywords: 11K45;11K06, 11K36,11J71, [MATH]Mathematics [math], [en] Correlation, well-distribution, generalized polynomials, binary sequence, pseudorandom
Funding:
    Source : HAL
  • Représentations, systèmes dynamiques et pavages; Funder: French National Research Agency (ANR); Code: ANR-18-CE40-0018
  • Dynamique symbolique et développements arithmétiques; Funder: French National Research Agency (ANR); Code: ANR-23-CE40-0024