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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)
The conference " Coding Theory " intended to be a platform where the rather inhomo-geneous coding community could exchange ideas. Both the engineers could present their mathematical problems and the mathematicians could report their progress. The result was a lively meeting with an open exchange of ideas and lots of discussion. Madhu Sudan presented his(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)
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)