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Extending MDS Codes
T.L. Alderson
Department of Mathematical Sciences, University of New Brunswick, Saint John, Canada
Annals of Combinatorics 9 (2) p.125-135 June, 2005
AMS Subject Classification: 94B25, 51E21, 05B15
A q-ary (n, k)-MDS code, linear or not, satisfies . A code meeting this bound is said to have maximum length. Using purely combinatorial methods we show that an MDS code with can be uniquely extended to a full length code if and only if q is even. This result is best possible in the sense that there is, for example, a non-extendable 4-ary (5, 4)-MDS code. It may be that the proof of our result is as interesting as the result itself. We provide a simple necessary and sufficient condition (property P) for code extendability. In future work, this condition might be suitably modified to give an extendability condition for arbitrary (shorter) MDS codes.
Keywords: MDS code, Latin hypercube, code extension


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