Classification of Graeco‐Latin Cubes |
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| Authors: | Janne I Kokkala Patric R J Östergård |
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| Institution: | 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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