— We investigate unramified coverings of algebraic curves over a finite field, specially in relation with maximal curves and the question whether maximal curves are covered by the Hermitian curve. Résumé (Sur les revêtements non-ramifiés des courbes maximales). — Nous étudions les revêtements non-ramifiés de courbes algébriques sur un corps fini, en particulier de courbes maximales. Nous nous p...

In this paper we solve three open problems on maximal curves with Frobenius dimension 3. In particular, we prove the existence of a maximal curve with order sequence (0, 1, 3, q).

We study geometrical properties of maximal curves having classical Weierstrass gaps.

In general, this bound is sharp. In fact if q is a square, there exist several curves that attain the above upper bound (see [4], [5], [14] and [23]). We say a curve is maximal (resp. minimal) if it attains the above upper (resp. lower) bound. There are however situations in which the bound can be improved. For instance, if q is not a square there is a non-trivial improvement due to Serre (see ...

Some linear codes associated to maximal algebraic curves via Feng-Rao construction [3] are investigated. In several case, these codes have better minimum distance with respect to the previously known linear codes with same length and dimension.

Let t --> gamma(t), 0 </= t </= 1, be a smooth curve in IR(n). Define the maximal function [unk](f) by [unk](f)(x) = sup(0<h</=1) (1/h) (0) (h) f(x - gamma(t)) dt. We state conditions under which parallel[unk](f) parallel(p) </= A(p) parallelf parallel(p), for 1 < p </= infinity.

Article history: Received 24 June 2008 Revised 29 January 2009 Available online 27 February 2009 Communicated by H. Stichtenoth This note contains general remarks concerning finite fields over which a so-called maximal, hyperelliptic curve of genus 3 exists. Moreover, the geometry of some specific hyperelliptic curves of genus 3 arising as quotients of Fermat curves, is studied. In particular, ...

The existence of a dense linear manifold of holomorphic functions on a Jordan domain having except for zero maximal cluster set along any curve tending to the boundary with nontotal oscillation value set is shown.

where C(Fq) denotes the set of Fq-rational points of the curve C. Here we will be interested in maximal(resp. minimal) curves over Fq2 , that is, we will consider curves C attaining Hasse-Weil’s upper (resp. lower) bound: #C(Fq2) = q + 1 + 2gq (resp. q + 1− 2gq). Here we are interested to consider the hyperelliptic curve C given by the equation y = x + 1 over Fq2 . We are going to determine whe...

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 MinT’s tables [1] are obtained.