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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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https://hal.archives-ouvertes.fr/hal-01779804
Contributor : Alicia Benson-Rumiz Connect in order to contact the contributor
Submitted on : Friday, April 27, 2018 - 12:09:02 AM
Last modification on : Wednesday, March 9, 2022 - 11:46:08 PM

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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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