Linear Codes Obtained from Projective and Grassmann Bundles on Curves

Abstract

We use split vector bundles on an arbitrary smooth curve defined over F_q 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 F_q and a p-semistable vector bundle E on C such that rank(E) = r, deg(E) = d and E is defined over F_q. Most results for particular curves are obtained taking double coverings or triple coverings of elliptic curves.