# 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} }

## 9 Citations

On the number of irreducible linear transformation shift registers

- MathematicsDes. 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

- Mathematics
- 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

- Computer Science, MathematicsJournal 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.

A note on the multiple-recursive matrix method for generating pseudorandom vectors

- Computer ScienceDiscret. Appl. Math.
- 2017

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

- MathematicsJournal 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 ScienceCryptography 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

- Mathematics
- 2019

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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