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

  • Authors:

  • T. L. Alderson

  • Affiliations:

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

  • Venue:
  • Designs, Codes and Cryptography
  • Year:
  • 2006

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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 驴 q+k驴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.