Arnaldo Garcia

A tower of Artin-Schreier extensions of function fields, attaining the Drinfeld-Vladut bound

SummaryFor an algebraic function fieldF having a finite constant field, letg(F) (resp.N(F)) denote the genus ofF (resp. the number of places ofF of degree one). We construct a tower of function fields

Elementary Abelianp-extensions of algebraic function fields

F_1 \subseteq F_2 \subseteq F_3 \subseteq \ldots

An explicit tower of function fields over cubic finite fields and Zink`s lower bound

over

Curves over Finite Fields Attaining the Hasse-Weil Upper Bound

\mathbb{F}_{q^2 }

Skew Pyramids of Function Fields Are Asymptotically Bad

such that the ratioN(Fi)/g(Fi) tends to the Drinfeld-Vladut boundq−1.

On Certain Subcovers of the Hermitian Curve

Abstract 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.