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Isometry invariant permutation codes and mutually orthogonal Latin squares
Author(s) -
Janiszczak Ingo,
Staszewski Reiner
Publication year - 2019
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21661
Subject(s) - mathematics , isometry group , permutation (music) , combinatorics , isometry (riemannian geometry) , invariant (physics) , permutation matrix , latin square , separable space , permutation group , discrete mathematics , pure mathematics , mathematical physics , circulant matrix , mathematical analysis , rumen , physics , chemistry , food science , fermentation , acoustics
Commonly, the direct construction and the description of mutually orthogonal Latin squares (MOLS) make use of difference or quasi‐difference matrices. Now there exists a correspondence between MOLS and separable permutation codes. We present separable permutation codes of length 35 , 48 , 63 , and 96 and minimum distance 34 , 47 , 62 , and 95 consisting of 6 × 35 , 10 × 48 , 8 × 63 , and 8 × 96 codewords, respectively. Using the correspondence, this gives 6 MOLS for n = 35 , 10 MOLS for n = 48 , 8 MOLS for n = 63 , and 8 MOLS for n = 96 . The codes are given by generators of an appropriate subgroup U of the isometry group of the symmetric group S n and U ‐orbit representatives. This gives an alternative uniform way to describe the MOLS.