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


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.

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.