(6,3)-MDS Codes over an Alphabet of Size 4
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An (n,k) q -MDS code C over an alphabet \(\cal A\) (of size q) is a collection of q k 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.
KeywordsMDS Code Bruen–Silverman Code dual arc
1991 Mathematics Subject Classification94B25 51E14
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