Related papers: Algebraic-geometric codes with many automorphisms …
Algebraic geometry codes or Goppa codes are defined with places of degree one. In constructing generalised algebraic geometry codes places of higher degree are used. In this paper we present 41 new codes over GF(16) which improve on the…
Let $K$ be a field of characteristic different from $2$ and let $E$ be an elliptic curve over $K$, defined either by an equation of the form $y^{2} = f(x)$ with degree $3$ or as the Jacobian of a curve defined by an equation of the form…
In this paper we systematically consider various ways of generating integrable and separable Hamiltonian systems in canonical and in non-canonical representations from algebraic curves on the plane. In particular, we consider St\"ackel…
Motivated by applications of algebraic geometry, we introduce the Galois width, a quantity characterizing the complexity of solving algebraic equations in a restricted model of computation allowing only field arithmetic and adjoining…
We characterize plane rational curves of degree four with two or more inner Galois points. A computer verifies the existence of plane rational curves of degree four with three inner Galois points. This would be the first example of a curve…
We investigate the arithmetic of algebraic curves on coarse moduli spaces for special linear rank two local systems on surfaces with fixed boundary traces. We prove a structure theorem for morphisms from the affine line into the moduli…
A criterion for the existence of a birational embedding with two Galois points for quotient curves is presented. We apply our criterion to several curves, for example, some cyclic subcovers of the Giulietti-Korchmaros curve or of the curves…
We continue the study of Hopf-Galois extensions with central invariants for a finite dimensional Hopf algebra. We concentrate on the geometrical side on the subject. We understand how to localize Hopf-Galois extensions and to paste them…
This survey is about Galois theory of curves in characteristic p, a topic which has inspired major research in algebraic geometry and number theory and which contains many open questions. We illustrate important phenomena which occur for…
The development of computational techniques in the last decade has made possible to attack some classical problems of algebraic geometry. In this survey, we briefly describe some open problems related to algebraic curves which can be…
Algebraic Geometric codes associated to a recently discovered class of maximal curves are investigated. As a result, some linear codes with better parameters with respect to the previously known ones are discovered, and 70 improvements on…
The Galois hull of a linear code is the intersection of itself and its Galois dual code, which has aroused the interest of researchers in these years. In this paper, we study Galois hulls of linear codes. Firstly, the symmetry of the…
This paper is a general survey of literature on Goppa-type codes from higher dimensional algebraic varieties. The construction and several techniques for estimating the minimum distance are described first. Codes from various classes of…
Automatic code generation for low-dimensional geometric algorithms is capable of producing efficient low-level software code through a high-level geometric domain specific language. Geometric Algebra (GA) is one of the most suitable…
This paper presents a new characterisation of the Fermat curve, according to the arrangement of Galois points.
Given an elliptic curve E over a number field k, the Galois action on the torsion points of E induces a Galois representation, \rho_E : Gal(\bar{k}/k) \to GL_2(\hat{Z}). For a fixed number field k, we describe the image of \rho_E for a…
We construct extensions of the field of rational numbers with the Galois group G_2(F_p) by reducing p-adic representations attached to automorphic representations.
In this paper we determine automorphism groups of cyclic algebraic curves defined over finite fields of any characteristic.
We give a method of constructing self-orthogonal codes from equitable partitions of association schemes. By applying this method we construct self-orthogonal codes from some distance-regular graphs. Some of the obtained codes are optimal.…
In a previous paper, the potential automorphy of certain Galois representations to GL_n for n even was established, following work of Harris, Shepherd-Barron and Taylor and using the lifting theorems of Clozel, Harris and Taylor. In this…