Characterization of sporadic perfect polynomials over \(\mathbb{F}_2\)

DOI10.7169/facm/2016.55.1.1zbMath1407.11140OpenAlexW2522017973MaRDI QIDQ1745208

Olivier Rahavandrainy, Luis H. Gallardo

Publication date: 20 April 2018

Published in: Functiones et Approximatio. Commentarii Mathematici (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.facm/1474301226

zbMATH Keywords

finite fieldspolynomialssum of divisorscharacteristic 2

Mathematics Subject Classification ID

Polynomials over finite fields (11T06) Arithmetic theory of polynomial rings over finite fields (11T55)

Related Items

Unnamed Item, Some families of unitary perfect polynomials over \(\mathbb{F}_2\), On the index of special perfect polynomials, Unnamed Item, Unnamed Item, On Mersenne polynomials over \(\mathbb{F}_2\), Fixed points of the sum of divisors function on \({{\mathbb{F}}}_2[x\)]

Cites Work

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• On even (unitary) perfect polynomials over \(\mathbb F_2\)
• Parity of the number of irreducible factors for composite polynomials
• There is no odd perfect polynomial over \(\mathbb F_{2}\) with four prime factors
• Odd perfect polynomials over \(\mathbb F_2\)
• The sum of the divisors of a polynomial
• Even perfect polynomials over $F_2$ with four prime factors