## Abstract

Let 𝓒 be a plane curve defined over the algebraic closure *K* of a finite prime field 𝔽_{p} by a separated polynomial, that is 𝓒 : *A*(*Y*) = *B*(*X*), where *A*(*Y*) is an additive polynomial of degree *p ^{n}* 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 𝓒 when

*m*≢ 1 mod

*p*and

^{n}*B*(

*X*) =

*X*. Moreover, some sufficient conditions for the automorphism group of 𝓒 to imply that

^{m}*B*(

*X*) =

*X*are provided. Also, the full automorphism group of the norm-trace curve 𝓒 :

^{m}*X*

^{(qr – 1)/(q–1)}=

*Y*

^{qr–1}+

*Y*

^{qr–2}+ … +

*Y*is computed. Finally, these results are used to show that certain one-point AG codes have many automorphisms.

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