Perfect Multiple Coverings in Metric Schemes
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 wordsperfect multiple covering metric scheme perfect code distance regular graph t-design orthogonal array
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