Linear Codes Obtained from Projective and Grassmann Bundles on Curves

Abstract

We use split vector bundles on an arbitrary smooth curve defined over Fq to get linear codes (following the general set-up considered by S. H. Hansen and T. Nakashima), generalizing two quoted results by T. Nakashima. If p ≠ 2 for all integers d, g ≥ 2, r > 0 such that either r is odd or d is even we prove the existence of a smooth curve C of genus g defined over Fq and a p-semistable vector bundle E on C such that rank(E) = r, deg(E) = d and E is defined over Fq. Most results for particular curves are obtained taking double coverings or triple coverings of elliptic curves.