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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
