Geodesic
Bounds on permutation codes of distance four
Journal of Algebraic Combinatorics, Tome 31 (2010) no. 1, pp. 143-158.

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Summary: A permutation code of length $n$ and distance $d$ is a set $\Gamma $of permutations from some fixed set of $n$ symbols such that the Hamming distance between each distinct $x, y\in \Gamma $is at least $d$. In this note, we determine some new results on the maximum size of a permutation code with distance equal to 4, the smallest interesting value. The upper bound is improved for almost all $n$ via an optimization problem on Young diagrams. A new recursive construction improves known lower bounds for small values of $n$.
Keywords: keywords symmetric group, permutation code, permutation array, characters, Young diagram, linear programming 
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     author = {Dukes, P. and Sawchuck, N.},
     title = {Bounds on permutation codes of distance four},
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     url = {http://geodesic.mathdoc.fr/item/JAC_2010__31_1_a1/}
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Dukes, P.; Sawchuck, N. Bounds on permutation codes of distance four. Journal of Algebraic Combinatorics, Tome 31 (2010) no. 1, pp. 143-158. http://geodesic.mathdoc.fr/item/JAC_2010__31_1_a1/