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Counting Irreducible Polynomials over Finite Fields Using the Inclusion-Exclusion Principle

2011/11/21 by Sunil K. Chebolu, Ján Mináč · 1 citation
Computer Science · #Coding theory and cryptography #semigroups and automata theory #Cellular Automata and Applications

paper · doi:10.4169/math.mag.84.5.369

openalex publication_date 2011/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

SummaryC. F. Gauss discovered a beautiful formula for the number of irreducible polynomials of a given degree over a finite field. Using just very basic knowledge of finite fields and the inclusion-exclusion formula, we show how one can see the shape of this formula and its proof almost instantly.

Citations

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