2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/134346The main conjecture on maximum distance separable (MDS) codes states that, execpt for some special cases, the maximum length of a q-ary linear MDS code is q+1. This conjecture does not hold true for near maximum distance separable codes because of the existence of q-ary near MDS elliptic codes having length bigger than q+1. An interesting related question is whether a near MDS elliptic code can be extended to a longer near MDS code. Our results are some non-extendability results and an alternative and simpler construction for certain known near MDS elliptic codes.Latex 2e, 13 pagesAlgebraic GeometryInformation TheoryCombinatorics51E22;14H52text