Constructions of Pairs of Orthogonal Latin Cubes

Abstract

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

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

References in corpus (1)

• The existence of designs II

Cited by in corpus (3)

• Diagonal groups and arcs over groups
• Toward a Three-dimensional Counterpart of Cruse's Theorem
• Embedding in MDS codes and Latin cubes