# An asymptotic formula for the number of irreducible transformation shift registers

@article{Cohen2015AnAF,
title={An asymptotic formula for the number of irreducible transformation shift registers},
author={Stephen D. Cohen and Sartaj Ul Hasan and Daniel Panario and Qiang Wang},
journal={ArXiv},
year={2015},
volume={abs/1506.02548}
}
• Published 8 June 2015
• Mathematics
• ArXiv
9 Citations
On the number of irreducible linear transformation shift registers
• Mathematics
Des. Codes Cryptogr.
• 2017
This work finds a bijection between Ram’s set to another set of irreducible polynomials which is easier to count, and gives a conjecture about the number of irReducible TSRs of any order.
Irreducible polynomials from a cubic transformation
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• 2021
Let R(x) = g(x)/h(x) be a rational expression of degree three over the finite field Fq. We count the irreducible polynomials in Fq[x], of a given degree, which have the form h(x) f · f ( R(x) ) for
Primitive transformation shift registers over finite fields
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Journal of Algebra and Its Applications
• 2019
This work considers systems which are efficient generalizations of LFSRs and produce pseudorandom vector sequences and gives certain results in this direction.
Cubic rational expressions over a finite field
• Mathematics
• 2021
We classify the cubic rational expressions g(x)/h(x) over a finite field, having at most three ramification points, under an equivalence relation given by preand post-composition with independent
Unimodular polynomial matrices over finite fields
• Mathematics
Journal of Algebraic Combinatorics
• 2020
We consider some combinatorial problems on matrix polynomials over finite fields. Using results from control theory, we give a proof of a result of Lieb, Jordan and Helmke on the number of linear
Nonlinear vectorial primitive recursive sequences
• Mathematics, Computer Science
Cryptography and Communications
• 2017
The nonlinearly filtered multiple-recursive matrix generator for producing pseudorandom vectors based on some nonlinear schemes is considered and lower bounds for their componentwise linear complexity are given.
Скрученные $\sigma$-разделимые линейные рекуррентные последовательности максимального периода
• Matematicheskie Voprosy Kriptografii [Mathematical Aspects of Cryptography]
• 2022
Пусть $p$ - простое число, $R=\mathrm{GR}(q^d,p^d)$ - кольцо Галуа мощности $q^d$ и характеристики $p^d$, где $q = p^r$, $S=\mathrm{GR}(q^{nd},p^d)$ - расширение степени $n$ кольца $R$, $\sigma$ -
Simple Linear Transformations 3 3 . Splitting Subspaces 7 4 . Density of Unimodular Polynomial Matrices 9
Abstract. We consider some combinatorial problems on matrix polynomials over finite fields. Using results from control theory we give a proof of a result of Helmke, Jordan and Lieb on the number of

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