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}
}
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9 Citations
Highly Influential Citations
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9 Citations

On the number of irreducible linear transformation shift registers
TLDR
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
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
TLDR
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
Cubic rational expressions over a finite field
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
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
TLDR
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
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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