# Arnaldo Garcia

We prove that if there are consecutive gaps at a rational point on a smooth curve defined over a finite field, then one can improve the usual lower bound on the minimum distance of certain algebraic-geometric codes defined using a multiple of the point. A q-ary linear code of length n and dimension k is a vector subspace of dimension k of F n q , where F q(More)
We study arithmetical and geometrical properties of maximal curves, that is, curves defined over the finite field F q 2 whose number of F q 2-rational points reaches the Hasse-Weil upper bound. Under a hypothesis on non-gaps at a rational point, we prove that maximal curves are F q 2-isomorphic to y q + y = x m , for some m ∈ Z +. As a consequence we show(More)
We present a new explicit tower of function fields (F n) n≥0 over the finite field with = q 3 elements, where the limit of the ratios (number of rational places of F n)/(genus of F n) is bigger or equal to 2(q 2 − 1)/(q + 2). This tower contains as a subtower the tower which was introduced by Bezerra– Garcia–Stichtenoth (see [3]), and in the particular case(More)
Let C be a (non-singular, projective, geometrically irreducible, algebraic) curve of genus g defined over a finite field F q with q elements. We know after A. Weil that the number of F q-points of a curve of genus g defined over F q satisfies the following limitations: q + 1 − 2g √ q ≤ #C(F q) ≤ 1 + q + 2g √ q, where C(F q) denotes the set of F q-rational(More)
Towers of function fields (resp., of algebraic curves) with positive limit provide examples of curves with large genus having many rational points over a finite field. It is in general a difficult task to calculate the genus of a wild tower. In this paper, we present a method for calculating the genus of certain Artin–Schreier towers. As an illustration of(More)