Embedding in MDS codes and Latin cubes. Issue 9 (20th June 2022)

• Record Type: Journal Article
• Authors: Potapov, Vladimir N.
• Is Part Of: Journal of combinatorial designs. Volume 30:Issue 9(2022)
• Page Start: 626
• Page End: 633
• Publication Date: 2022-06-20
• Subjects: embedding -- Latin cube -- Latin square -- MDS code -- MOLS; Combinatorial designs and configurations -- Periodicals; Configurations et schémas combinatoires -- Périodiques; 511.6
• DOI: 10.1002/jcd.21849
• Languages: English
• ISSNs: 1063-8539

Abstract

Abstract: An embedding of a code is a mapping that preserves distances between codewords. We prove that any code with code distance d $d$ and length n $n$ can be embedded into an maximum distance separable (MDS) code with the same code distance and length but under a larger alphabet. As a corollary we obtain embeddings of systems of partial mutually orthogonal Latin cubes and n $n$ ‐ary quasigroups.