Linear Codes Obtained from Projective and Grassmann Bundles on Curves

  • Edoardo Ballico Department of Mathematics, University of Trento, 38123 Povo (TN), Italy
Keywords: vector bundles on curves, linear code, projective bundle, Grassmann code, p-semistable vector bundle

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.

Published
2020-07-22
How to Cite
Ballico, E. (2020) “Linear Codes Obtained from Projective and Grassmann Bundles on Curves”, Contemporary Mathematics, 1(4). doi: 10.37256/cm.142020449.