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Let C be a curve of genus 2 and ψ1 : C −→ E1 a map of degree n, from C to an elliptic curve E1, both curves defined over C. This map induces a degree n map φ1 : P 1 −→ P 1 which we call a Frey-Kani covering. We determine all possible ramifications for φ1. If ψ1 : C −→ E1 is maximal then there exists a maximal map ψ2 : C −→ E2, of degree n, to some elliptic(More)
Let G be a finite group, and g ≥ 2. We study the locus of genus g curves that admit a G-action of given type, and inclusions between such loci. We use this to study the locus of genus g curves with prescribed automorphism group G. We completely classify these loci for g = 3 (including equations for the corresponding curves), and for g ≤ 10 we classify those(More)
We introduce a new approach of computing the automorphism group and the field of moduli of points p = [C] in the moduli space of hyperel-liptic curves Hg. Further, we show that for every moduli point p ∈ Hg(L) such that the reduced automorphism group of p has at least two involu-tions, there exists a representative C of the isomorphism class p which is(More)
Let X be an algebraic curve of genus g 2 defined over a field Fq of characteristic p > 0. From X , under certain conditions, we can construct an algebraic geometry code C. If the code C is self-orthogonal under the symplectic product then we can construct a quantum code Q, called a QAG-code. In this paper we study the construction of such codes from curves(More)
We study C a,b curves and their applications to coding theory. Recently, Joyner and Ksir have suggested a decoding algorithm based on the automorphisms of the code. We show how C a,b curves can be used to construct MDS codes and focus on some C a,b curves with extra automorphisms, namely y 3 = x 4 + 1, y 3 = x 4 − x, y 3 − y = x 4. The automorphism groups(More)