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A trigonometric approach for Dickson polynomials over fields of characteristic two

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Abstract

In this paper, we first introduce a trigonometric approach for Dickson polynomials of the first and the second kinds over fields of characteristic two. Employing the proposed concepts, we revisit known properties of such polynomials. Additionally, we derive new results regarding the fixed points and the involutive behavior of Dickson polynomials of the second kind over \({\mathbb {F}}_{2^n}\).

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Notes

  1. We remark that, differently from what occurs in finite fields of odd characteristic, of course, the finite field cosine in fields of characteristic two does not have a division by two in its definition.

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Acknowledgements

This work was supported in part by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) under Grants 309598/2017-6 and 409543/2018-7, by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) under Grant 88881.311848/2018-01, and by NSERC Canada.

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Authors and Affiliations

  1. Department of Electronics and Systems, Federal University of Pernambuco, Recife, Brazil

    Juliano B. Lima

  2. School of Mathematics and Statistics, Carleton University, Ottawa, Canada

    Daniel Panario

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  1. Juliano B. Lima
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  2. Daniel Panario
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Correspondence to Daniel Panario.

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Lima, J.B., Panario, D. A trigonometric approach for Dickson polynomials over fields of characteristic two. AAECC 31, 253–270 (2020). https://doi.org/10.1007/s00200-020-00429-9

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