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arXiv · 0801.3983

New Upper Bounds on Sizes of Permutation Arrays

Lizhen Yang·Ling Dong·Kefei Chen
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Abstract

A permutation array(or code) of length $n$ and distance $d$, denoted by $(n,d)$ PA, is a set of permutations $C$ from some fixed set of $n$ elements such that the Hamming distance between distinct members $\mathbf{x},\mathbf{y}\in C$ is at least $d$. Let $P(n,d)$ denote the maximum size of an $(n,d)$ PA. New upper bounds on $P(n,d)$ are given. For constant $α,β$ satisfying certain conditions, whenever $d=βn^α$, the new upper bounds are asymptotically better than the previous ones.

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Lizhen Yang, Ling Dong, Kefei Chen. 2008-01-25. New Upper Bounds on Sizes of Permutation Arrays. https://arxiv.org/abs/0801.3983

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