A lower bound on permutation codes of distance n-1

A classical recursive construction for mutually orthogonal latin squares (MOLS) is shown to hold more generally for a class of permutation codes of length n and minimum distance n - 1 . When such codes of length p + 1 are included as ingredients, we obtain a general lower bound M ( n , n - 1 ) ≥ n 1...

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Veröffentlicht in:	Designs, codes, and cryptography codes, and cryptography, 2020, Vol.88 (1), p.63-72
Hauptverfasser:	Bereg, Sergey, Dukes, Peter J.
Format:	Artikel
Sprache:	eng
Schlagworte:	Arrays Circuits Codes Coding and Information Theory Computer Science Cryptology Data Structures and Information Theory Discrete Mathematics in Computer Science Information and Communication Latin square design Lower bounds Permutations
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Zusammenfassung:	A classical recursive construction for mutually orthogonal latin squares (MOLS) is shown to hold more generally for a class of permutation codes of length n and minimum distance n - 1 . When such codes of length p + 1 are included as ingredients, we obtain a general lower bound M ( n , n - 1 ) ≥ n 1.0797 for large n , gaining a small improvement on the guarantee given from MOLS.
ISSN:	0925-1022 1573-7586
DOI:	10.1007/s10623-019-00670-5