A lower bound on permutation codes of distance n-1

2019/02/11 by Sergey Bereg, Bereg, Sergey, Peter Dukes +1
Mathematics · #05B15 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05B15

paper · pdf · doi:10.48550/arxiv.1902.04153

arxiv created 2019/07/31 · arxiv updated 2019/08/02

Abstract

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^1.079 for large n, gaining a small improvement on the guarantee given from MOLS.

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