Constructions of Pairs of Orthogonal Latin Cubes

Vladimir N. Potapov

doi:10.1002/jcd.21718

Constructions of Pairs of Orthogonal Latin Cubes

Combinatorics 2023-03-30 v2 Information Theory math.IT

Authors: Vladimir N. Potapov

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Abstract

A pair of orthogonal latin cubes of order $q$ is equivalent to an MDS code with distance $3$ or to an ${\rm OA}_1(3,5,q)$ orthogonal array. We construct pairs of orthogonal latin cubes for a sequence of previously unknown orders $q_i=16(18i-1)+4$ and $q'_i=16(18i+5)+4$ . The minimal new obtained parameters of orthogonal arrays are ${\rm OA}_1(3,5,84)$ . Keywords: latin square, latin cube, MOLS, MDS code, block design, Steiner system, orthogonal array

Keywords

orthogonal latin cubes latin square mds code block design steiner system orthogonal array

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@article{arxiv.1911.12960,
  title  = {Constructions of Pairs of Orthogonal Latin Cubes},
  author = {Vladimir N. Potapov},
  journal= {arXiv preprint arXiv:1911.12960},
  year   = {2023}
}

Comments

New pairs of orthogonal latin 3-cubes are available on the website https://ieee-dataport.org/open-access/graeco-latin-cubes

Constructions of Pairs of Orthogonal Latin Cubes

Abstract

Keywords

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