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arXiv · 1005.5591

On the minimum weight problem of permutation codes under Chebyshev distance

Min-Zheng Shieh·Shi-Chun Tsai
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Abstract

Permutation codes of length $n$ and distance $d$ is a set of permutations on $n$ symbols, where the distance between any two elements in the set is at least $d$. Subgroup permutation codes are permutation codes with the property that the elements are closed under the operation of composition. In this paper, under the distance metric $\ell_{\infty}$-norm, we prove that finding the minimum weight codeword for subgroup permutation code is NP-complete. Moreover, we show that it is NP-hard to approximate the minimum weight within the factor $7/6-ε$ for any $ε>0$.

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Min-Zheng Shieh, Shi-Chun Tsai. 2010-05-31. On the minimum weight problem of permutation codes under Chebyshev distance. https://arxiv.org/abs/1005.5591

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