On even (unitary) perfect polynomials over \(\mathbb F_2\)

DOI10.1016/J.FFA.2012.06.004zbMath1273.11175OpenAlexW2008981867MaRDI QIDQ714457

Olivier Rahavandrainy, Luis H. Gallardo

Publication date: 11 October 2012

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ffa.2012.06.004

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 (7)

Unnamed Item ⋮ Some families of unitary perfect polynomials over \(\mathbb{F}_2\) ⋮ On perfect polynomials over \(\mathbb{F}_p\) with \(p\) irreducible factors ⋮ On the index of special perfect polynomials ⋮ Characterization of sporadic perfect polynomials over \(\mathbb{F}_2\) ⋮ On Mersenne polynomials over \(\mathbb{F}_2\) ⋮ Fixed points of the sum of divisors function on \({{\mathbb{F}}}_2[x\)]

Cites Work

• All unitary perfect polynomials over \(\mathbb F_2\) with at most four distinct irreducible factors
• Unitary perfect polynomials over \(\mathbb {F}_4\) with less than five prime factors
• There is no odd perfect polynomial over \(\mathbb F_{2}\) with four prime factors
• On the square-freeness of Fermat and Mersenne numbers
• 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
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