New upper bounds for the size of permutation codes via linear programming
The electronic journal of combinatorics, Tome 17 (2010)
An $(n,d)$-permutation code of size $s$ is a subset $C$ of $S_n$ with $s$ elements such that the Hamming distance $d_H$ between any two distinct elements of $C$ is at least equal to $d$. In this paper, we give new upper bounds for the maximal size $\mu(n,d)$ of an $(n,d)$-permutation code of degree $n$ with $11\le n\le 14$. In order to obtain these bounds, we use the structure of association scheme of the permutation group $S_n$ and the irreducible characters of $S_n$. The upper bounds for $\mu(n,d)$ are determined solving an optimization problem with linear inequalities.
DOI :
10.37236/407
Classification :
05B15, 05E30, 90C05
Mots-clés : permutation code, Hamming distance, association scheme, permutation group
Mots-clés : permutation code, Hamming distance, association scheme, permutation group
@article{10_37236_407,
author = {Mathieu Bogaerts},
title = {New upper bounds for the size of permutation codes via linear programming},
journal = {The electronic journal of combinatorics},
year = {2010},
volume = {17},
doi = {10.37236/407},
zbl = {1204.05030},
url = {http://geodesic.mathdoc.fr/articles/10.37236/407/}
}
Mathieu Bogaerts. New upper bounds for the size of permutation codes via linear programming. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/407
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