Scroll codes over curves of higher genus
We construct linear codes from scrolls over curves of high genus and study the higher support weights d(i) of these codes. We embed the scroll into projective space P(k-1) and calculate bounds for the d(i) by considering the maximal number of F(q)-rational points that are contained in a codimension h subspace of P(k-1). We find lower bounds of the d(i) and for the cases of large i calculate the exact values of the d(i). This work follows the natural generalisation of Goppa codes to higher-dimensional varieties as studied by S. H. Hansen, C. Lomont and T. Nakashima.
projective bundles on curves error-correcting codes