A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vladut bound.
Automorphism groups of Ree type Deligne-Lusztig curves and function fields.
Codes and projective multisets.
Codes from cubic curves and their extensions.
Determinants of Legendre symbol matrices
Differential approach for the study of duals of algebraic-geometric codes on surfaces
The purpose of the present article is the study of duals of functional codes on algebraic surfaces. We give a direct geometrical description of them, using differentials. Even if this description is less trivial, it can be regarded as a natural extension to surfaces of the result asserting that the dual of a functional code on a curve is the differential code . We study the parameters of such codes and state a lower bound for their minimum distance. Using this bound, one can study some examples...
Elementary Albeian p-Extensions of Algebraic Function Fields.
Families of nets of low and medium strength.
Finite geometries, varieties and codes.
Konische Codes auf eigenen Überdeckungskurven.
Nets, -sequences, and algebraic curves over finite fields with many rational points.
New optimal constant weight codes.
On a class of constant weight codes.
On optimal linear codes over .
On the Automorphism Groups of some AG-Codes Based on Ca;b Curves
*Partially supported by NATO.We study Ca,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 Ca;b curves can be used to construct MDS codes and focus on some Ca;b curves with extra automorphisms, namely y^3 = x^4 + 1, y^3 = x^4 - x, y^3 - y = x^4. The automorphism groups of such codes are determined in most characteristics.
On the classification of 3-dimensional non-associative division algebras over -adic fields
Let be a prime and a -adic field (a finite extension of the field of -adic numbers ). We employ the main results in [12] and the arithmetic of elliptic curves over to reduce the problem of classifying 3-dimensional non-associative division algebras (up to isotopy) over to the classification of ternary cubic forms over (up to equivalence) with no non-trivial zeros over . We give an explicit solution to the latter problem, which we then relate to the reduction type of the jacobian...
On the Construction of Codes from an Asymptotically Good Tower over F8
In 2002, van der Geer and van der Vlugt gave explicit equations for an asymptotically good tower of curves over the field F8. In this paper, we will present a method for constructing Goppa codes from these curves as well as explicit constructions for the third level of the tower. The approach is to find an associated plane curve for each curve in the tower and then to use the algorithms of Haché and Le Brigand to find the corresponding Goppa codes.
Quadratic forms, fibre products and some plane curves with many points
Reed-Muller codes and supersingular curves. I
Réseaux quaternioniens et invariant de Venkov.