TY - JOUR AU - Ballico, E. PY - 2020/07/22 Y2 - 2024/03/28 TI - Linear Codes Obtained from Projective and Grassmann Bundles on Curves JF - Contemporary Mathematics JA - Contemp. Math. VL - 1 IS - 4 SE - Research Article DO - 10.37256/cm.142020449 UR - https://ojs.wiserpub.com/index.php/CM/article/view/449 SP - 187-191 AB - <p>We use split vector bundles on an arbitrary smooth curve defined over F<em><sub>q</sub></em> 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 <em>p</em> ≠ 2 for all integers <em>d</em>, <em>g</em> ≥ 2,<em> r</em> &gt; 0 such that either <em>r</em> is odd or <em>d</em> is even we prove the existence of a smooth curve <em>C</em> of genus <em>g</em> defined over F<em><sub>q </sub></em>and a <em>p-</em>semistable vector bundle <em>E</em> on <em>C</em> such that rank(<em>E</em>) = <em>r</em>, deg(<em>E</em>) = <em>d</em> and <em>E</em> is defined over F<em><sub>q</sub></em>. Most results for particular curves are obtained taking double coverings or triple coverings of elliptic curves.</p> ER -