2002/11/06 by Massimo Giulietti, Giulietti, Massimo
Computer Science · Mathematics · #Coding theory and cryptography #Cooperative Communication and Network Coding #Finite Group Theory Research
paper · pdf · doi:10.48550/arxiv.math/0211107
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.