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Permutation Binomial Functions over Finite Fields

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Abstract

We consider binomial functions over a finite field of order 2n. Some necessary condition is found for such a binomial function to be a permutation. It is proved that there are no permutation binomial functions in the case that 2n − 1 is prime. Permutation binomial functions are constructed in the case when n is composite and found for n ≥ 8.

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Authors and Affiliations

  1. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    A. V. Miloserdov

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  1. A. V. Miloserdov
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Correspondence to A. V. Miloserdov.

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Original Russian Text © A.V. Miloserdov, 2018, published in Diskretnyi Analiz i Issledovanie Operatsii, 2018, Vol. 25, No. 4, pp. 59–80.

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Miloserdov, A.V. Permutation Binomial Functions over Finite Fields. J. Appl. Ind. Math. 12, 694–705 (2018). https://doi.org/10.1134/S1990478918040105

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  • DOI: https://doi.org/10.1134/S1990478918040105

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