On algebraic curves with many automorphisms in characteristic p

Non-Genera of Curves With Automorphisms in Characteristic P

Quantum codes from algebraic curves with automorphisms

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 with automorphisms and the relation ...

Characteristic polynomials of automorphisms of hyperelliptic curves

Let α be an automorphism of a hyperelliptic curve C of genus g and let α be the automorphism induced by α on the genus-0 quotient of C by the hyperelliptic involution. Let n be the order of α and let n be the order of α. We show that the characteristic polynomial f of the automorphism α∗ of the Jacobian of C is determined by the values of n, n, and g, unless n = n, n is even, and (2g + 2)/n is ...

Automorphisms of Hyperelliptic Modular Curves X0(n) in Positive Characteristic

We study the automorphism groups of the reduction X0(N)× F̄p of a modular curve X0(N) over primes p ∤ N .

On large automorphism groups of algebraic curves in positive characteristic

In his investigation on large K-automorphism groups of an algebraic curve, Stichtenoth obtained an upper bound on the order of the first ramification group of an algebraic curve X defined over an algebraically closed field of characteristic p. Stichtenoth’s bound has raised the problem of classifying all K-automorphism groups G of X with the following property: There is a point P ∈ X for which ...