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Journal Articles Advances in Mathematics of Communications Year : 2014

On the irreducibility of the hyperplane sections of Fermat varieties in P3 in characteristic 2

Abstract

Let t be an integer ≥ 3 such that t ≡ 1 mod 4. The absolute irreducibility of the polynomial ϕt(x,y)=xt+yt+1+(x+y+1)t(x+y)(x+1)(y+1) (over F2) 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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hal-01779804 , version 1 (27-04-2018)

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Eric Férard. On the irreducibility of the hyperplane sections of Fermat varieties in P3 in characteristic 2. Advances in Mathematics of Communications, 2014, 8 (4), pp.497-509. ⟨10.3934/amc.2014.8.497⟩. ⟨hal-01779804⟩

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