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

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.

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