Three Proofs of an Observation on Irreducible Polynomials over $\text{GF}(2)$

Robert Granger

Three Proofs of an Observation on Irreducible Polynomials over $\text{GF}(2)$

Combinatorics 2023-02-24 v1

Authors: Robert Granger

Abstract

We present three proofs of an observation of Ahmadi on the number of irreducible polynomials over $\text{GF}(2)$ with certain traces and cotraces, the most interesting of which uses an explicit natural bijection. We also present two proofs of a related observation.

Keywords

irreducible polynomials GF(2) traces cotraces bijection finite fields

Cite

@article{arxiv.2302.11932,
  title  = {Three Proofs of an Observation on Irreducible Polynomials over $\text{GF}(2)$},
  author = {Robert Granger},
  journal= {arXiv preprint arXiv:2302.11932},
  year   = {2023}
}

Comments

8 pages, 1 table, accepted for publication in Finite Fields and Their Applications

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