Let be a plane curve defined over the algebraic closure K of a finite prime field p by a separated polynomial, that is : A(Y) = B(X), where A(Y) is an additive polynomial of degree pn and the degree m of B(X) is coprime with p. Plane curves given by separated polynomials are widely studied; however, their automorphism groups are not completely determined. In this paper we compute the full automorphism group of when m 1 mod pn and B(X) = Xm. Moreover, some sufficient conditions for the automorphism group of to imply that B(X) = Xm are provided. Also, the full automorphism group of the norm-trace curve : X(qr - 1)/(q-1) = Yqr-1 + Yqr-2 + ... + Y is computed. Finally, these results are used to show that certain one-point AG codes have many automorphisms.

On plane curves given by separated polynomials and their automorphisms

Zini G.
2020

Abstract

Let be a plane curve defined over the algebraic closure K of a finite prime field p by a separated polynomial, that is : A(Y) = B(X), where A(Y) is an additive polynomial of degree pn and the degree m of B(X) is coprime with p. Plane curves given by separated polynomials are widely studied; however, their automorphism groups are not completely determined. In this paper we compute the full automorphism group of when m 1 mod pn and B(X) = Xm. Moreover, some sufficient conditions for the automorphism group of to imply that B(X) = Xm are provided. Also, the full automorphism group of the norm-trace curve : X(qr - 1)/(q-1) = Yqr-1 + Yqr-2 + ... + Y is computed. Finally, these results are used to show that certain one-point AG codes have many automorphisms.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11591/415213
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