Original scientific paper

All perfect polynomials with up to four prime factors over $F_4$

Luis H. Gallardo ; Department of Mathematics, University of Brest 6, France
Olivier Rahavandrainy ; Department of Mathematics, University of Brest 6, France

Abstract

A perfect polynomial over the field $\F_4$ is a monic polynomial $A
\in \F_4[x]$ that equals the sum of all its monic divisors. If
$\gcd(A,x^4+x)=1$, then we say that $A$ is odd over $\F_4$. In this
paper, we characterize odd perfect polynomials over $\F_4$, with
four prime divisors. There follows a classification of all perfect
polynomials over $\F_4$ with up to four prime divisors.

Keywords

sum of divisors; polynomials; finite fields; characteristic 2

Hrčak ID:

37345

URI

https://hrcak.srce.hr/37345

Publication date:

3.6.2009.

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