Scroll codes over curves of higher genus

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