Some Maximal Function Fields and Additive Polynomials |
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Authors: | Arnaldo Garcia Ferruh Özbudak |
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Institution: | 1. Institute of Pure and Applied Mathematics , Rio de Janeiro, Brasil garcia@impa.br;3. Department of Mathematics , Middle East Technical University , In?nü Bulvari, Ankara, Turkey |
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Abstract: | We derive explicit equations for the maximal function fields F over 𝔽 q 2n given by F = 𝔽 q 2n (X, Y) with the relation A(Y) = f(X), where A(Y) and f(X) are polynomials with coefficients in the finite field 𝔽 q 2n , and where A(Y) is q-additive and deg(f) = q n + 1. We prove in particular that such maximal function fields F are Galois subfields of the Hermitian function field H over 𝔽 q 2n (i.e., the extension H/F is Galois). |
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Keywords: | Additive polynomial Finite field Maximal curve |
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