Classification of Graeco-Latin Cubes

DOI10.1002/jcd.21400zbMath1331.05044OpenAlexW1901731858MaRDI QIDQ5744161

Janne I. Kokkala, Patric R. J. Östergård

Publication date: 17 February 2016

Published in: Journal of Combinatorial Designs (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/jcd.21400

zbMATH Keywords

classificationLatin squareMOLSMDS codeGraeco-Latin cube

Mathematics Subject Classification ID

Orthogonal arrays, Latin squares, Room squares (05B15) Theory of error-correcting codes and error-detecting codes (94B99)

Related Items (6)

Construction of generalized minimum aberration three-level orthogonal arrays with three, four and five columns ⋮ Classification of MDS Codes over Small Alphabets ⋮ Further results on the classification of MDS codes ⋮ Integer Programming for Classifying Orthogonal Arrays ⋮ MDS codes in Doob graphs ⋮ Constructions of transitive Latin hypercubeatin hypercubes

Uses Software

• nauty
• Cliquer

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Strong forms of orthogonality for sets of hypercubes
• Classification algorithms for codes and designs
• Point sets with uniformity properties and orthogonal hypercubes
• Orthogonal hypercubes and related designs
• \(d\)-dimensional hypercubes and the Euler and MacNeish conjectures
• On the finite completion of partial latin cubes
• Practical graph isomorphism. II.
• (6,3)-MDS codes over an alphabet of size 4
• Latin hypercubes and MDS codes
• A Metrization for Power-Sets with Applications to Combinatorial Analysis
• Small latin squares, quasigroups, and loops
• A Census of Small Latin Hypercubes
• Atomic Latin squares of order eleven
• Optimal binary one-error-correcting codes of length 10 have 72 codewords
• The Perfect Binary One-Error-Correcting Codes of Length <formula formulatype="inline"><tex Notation="TeX">$15$</tex></formula>: Part I—Classification
• On Optimal Binary One-Error-Correcting Codes of Lengths $2^{m}-4$ and $2^{m}-3$
• Transversals in Latin Squares
• Maximum distance&lt;tex&gt;q&lt;/tex&gt;-nary codes
• THE RELATIONSHIP BETWEEN FINITE GROUPS AND COMPLETELY ORTHOGONAL SQUARES, CUBES, AND HYPER-CUBES

This page was built for publication: Classification of Graeco-Latin Cubes