Bounds on permutation codes of distance four |
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| Authors: | P. Dukes N. Sawchuck |
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| Affiliation: | (1) Chern Institute of Mathematics, Nankai University, Tianjin, 300071, People’s Republic of China;(2) Temasek Laboratories, National University of Singapore, 5 Sports Drive 2, Singapore, 117508, Singapore;(3) Graduate School at Shenzhen, Tsinghua University, Shenzhen, Guangdong, 518055, People’s Republic of China |
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| Abstract: | A permutation code of length n and distance d is a set Γ of permutations from some fixed set of n symbols such that the Hamming distance between each distinct x,y∈Γ 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. |
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