Classification of Graeco‐Latin Cubes |
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Authors: | Janne I. Kokkala Patric R. J. Östergård |
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Affiliation: | Department of Communications and Networking, Aalto University School of Electrical Engineering, Aalto, Finland |
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Abstract: | A q‐ary code of length n, size M, and minimum distance d is called an code. An code with is said to be maximum distance separable (MDS). Here one‐error‐correcting () MDS codes are classified for small alphabets. In particular, it is shown that there are unique (5, 53, 3)5 and (5, 73, 3)7 codes and equivalence classes of (5, 83, 3)8 codes. The codes are equivalent to certain pairs of mutually orthogonal Latin cubes of order q, called Graeco‐Latin cubes. |
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Keywords: | Latin square MOLS Graeco‐Latin cube MDS code classification |
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