[Some families of unitary perfect polynomials over ]
We characterize all the known unitary perfect binary polynomials by precising their admissible families. Our method allows us to find other ones.
Nous caractérisons les polynômes binaires unitairement parfaits, connus jusqu’ici, apparemment de façon « empirique » . La méthode que nous avons trouvée a permis et permettrait d’en découvrir d’autres.
Revised:
Accepted:
Published online:
Olivier Rahavandrainy 1

@article{CRMATH_2021__359_2_123_0, author = {Olivier Rahavandrainy}, title = {Familles de polyn\^omes unitairement parfaits sur $\protect \mathbb{F}_2$}, journal = {Comptes Rendus. Math\'ematique}, pages = {123--130}, publisher = {Acad\'emie des sciences, Paris}, volume = {359}, number = {2}, year = {2021}, doi = {10.5802/crmath.149}, language = {fr}, }
Olivier Rahavandrainy. Familles de polynômes unitairement parfaits sur $\protect \mathbb{F}_2$. Comptes Rendus. Mathématique, Volume 359 (2021) no. 2, pp. 123-130. doi : 10.5802/crmath.149. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.149/
[1] Unitary perfect polynomials over , Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat., Volume 62 (1977) no. 5, pp. 417-422 | MR | Zbl
[2] Infinitely many perfect and unitary perfect polynomials, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat., Volume 63 (1977) no. 5, pp. 294-303 | MR | Zbl
[3] The sum of the divisors of a polynomial, Duke Math. J., Volume 8 (1941), pp. 721-737 | DOI | MR | Zbl
[4] Odd perfect polynomials over , J. Théor. Nombres Bordeaux, Volume 19 (2007) no. 1, pp. 165-174 | DOI | Numdam | MR | Zbl
[5] Even perfect polynomials over with four prime factors, Int. J. Pure Appl. Math., Volume 52 (2009) no. 2, pp. 301-314 | MR
[6] There is no odd perfect polynomial over with four prime factors, Port. Math. (N.S.), Volume 66 (2009) no. 2, pp. 131-145 | DOI | MR | Zbl
[7] On even (unitary) perfect polynomials over , Finite Fields Appl., Volume 18 (2012) no. 5, pp. 920-932 | DOI | MR | Zbl
[8] Characterization of Sporadic perfect polynomials over , Funct. Approximatio, Comment. Math., Volume 55 (2016) no. 1, pp. 7-21 | DOI | MR | Zbl
[9] On Mersenne polynomials over , Finite Fields Appl., Volume 59 (2019), pp. 284-296 | DOI | MR | Zbl
[10] On odd prime divisors of binary perfect polynomials (2020) (https://arxiv.org/abs/2007.16016)
Cited by Sources:
Comments - Policy