Geodesic
New upper bounds for the size of permutation codes via linear programming
The electronic journal of combinatorics, Tome 17 (2010)

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Zbl EuDML
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 
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
@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/}
}
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