Abstract
A permutation code of length n and minimum distance d is a set Γ of permutations from some fixed set of n symbols such that the Hamming distance between any distinct \({u,v \in \Gamma}\) is at least d. As a generalization, we introduce the problem of packing injections from an m-set, m ≤ n, sometimes called m-arrangements, relative to Hamming distance. We offer some preliminary coding-theoretic bounds, a few design-theoretic connections, and a short discussion on possible applications.
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This is one of several papers published together in Designs, Codes and Cryptography on the special topic: “Combinatorics – A Special Issue Dedicated to the 65th Birthday of Richard Wilson”.
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Dukes, P.J. Coding with injections. Des. Codes Cryptogr. 65, 213–222 (2012). https://doi.org/10.1007/s10623-011-9547-4
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DOI: https://doi.org/10.1007/s10623-011-9547-4