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On Some Permutation Binomials and Trinomials Over F 2 n

Abstract : In this work, we completely characterize (i) permutation bi-nomials of the form f (x) = x^{( 2^n −1)/( 2^k −1) +1} + ax ∈ F2^n [x], k odd and n = 2^r k(r ≥ 1), a ∈ F *_{2^{2k}} , and (ii) permutation trinomials of the form x^{ 2^r +1} +x^{ 2^r−1} +1 +αx ∈ F _{2^k} [x], k odd. First result, which was our primary motivation, is a consequence of the second result. Second result may be of independent interest.
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https://hal.inria.fr/hal-01275776
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Srimanta Bhattacharya, Sumanta Sarkar. On Some Permutation Binomials and Trinomials Over F 2 n. WCC2015 - 9th International Workshop on Coding and Cryptography 2015, Anne Canteaut, Gaëtan Leurent, Maria Naya-Plasencia, Apr 2015, Paris, France. ⟨hal-01275776⟩

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