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On the irreducibility of the hyperplane sections of Fermat varieties in \(\mathbb {P}^{3}\) in characteristic 2. II

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Abstract

Let t be an integer ≥ 3 such that t ≡ 1 mod 4. The absolute irreducibility of the polynomial \(\phi _{t}(x, y) = \frac {x^{t} + y^{t} + 1 + (x + y + 1)^{t}}{(x + y)(x + 1)(y + 1)}\) (over \(\mathbb {F}_{2}\)) plays an important role in the study of APN functions. We prove that this polynomial is absolutely irreducible under the assumptions that the largest odd integer which divides t − 1 is large enough and can not be written in a specific form.

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  1. Équipe GAATI, Université de la Polynésie Française, Polynésie Française, France

    Eric Férard

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  1. Eric Férard
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Correspondence to Eric Férard.

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Férard, E. On the irreducibility of the hyperplane sections of Fermat varieties in \(\mathbb {P}^{3}\) in characteristic 2. II. Cryptogr. Commun. 9, 749–767 (2017). https://doi.org/10.1007/s12095-017-0213-1

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  • DOI: https://doi.org/10.1007/s12095-017-0213-1

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