Designs, Codes and Cryptography

, Volume 65, Issue 3, pp 213–222 | Cite as

Coding with injections

  • Peter J. Dukes


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.


Permutation code Injection Arrangement Ordered design Hamming distance 

Mathematics Subject Classification (2000)

Primary 05A05 94A10 Secondary 05B40 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Mathematics and StatisticsUniversity of VictoriaVictoriaCanada

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