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(6,3)-MDS Codes over an Alphabet of Size 4

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Abstract

An (n,k) q -MDS code C over an alphabet \(\cal A\) (of size q) is a collection of qk n–tuples over \(\cal A\) such that no two words of C agree in as many as k coordinate positions. It follows that n ≤ q+k−1. By elementary combinatorial means we show that every (6,3)4-MDS code, linear or not, turns out to be a linear (6,3)4-MDS code or else a code equivalent to a linear code with these parameters. It follows that every (5,3)4-MDS code over\(\cal A\) must also be equivalent to linear.

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  1. Mathematical Sciences, University of New Brunswick, Saint John, Canada, E2L 4L5

    T. L. Alderson

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  1. T. L. Alderson
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D. Jungnickel

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Alderson, T.L. (6,3)-MDS Codes over an Alphabet of Size 4. Des Codes Crypt 38, 31–40 (2006). https://doi.org/10.1007/s10623-004-5659-4

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  • DOI: https://doi.org/10.1007/s10623-004-5659-4

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