Perfect Multiple Coverings in Metric Schemes

  • Richard Clayton
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 20)


Perfect multiple coverings generalize the concept of perfect codes by allowing for multiplicities, much as t-designs generalize Steiner systems. A necessary and sufficient condition is found to determine when a metric scheme admits a nontrivial perfect multiple covering. Results specific to the classical Hamming and Johnson schemes are given which bear out the relationship between t-designs, orthogonal arrays, and perfect multiple coverings.

Key words

perfect multiple covering metric scheme perfect code distance regular graph t-design orthogonal array 


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Copyright information

© Springer-Verlag New York, Inc. 1990

Authors and Affiliations

  • Richard Clayton
    • 1
  1. 1.Department of MathematicsOhio State UniversityColumbusUSA

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