On Near-MDS Elliptic Codes
<|reference_start|>On Near-MDS Elliptic Codes: The 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.<|reference_end|>
@article{giulietti2002on,
    title={On Near-MDS Elliptic Codes},
    author={Massimo Giulietti},
    journal={arXiv preprint arXiv:math/0211107},
    year={2002},
    archivePrefix={arXiv},
    eprint={math/0211107},
    primaryClass={math.AG cs.IT math.CO math.IT}
}