A Note on Perfect Multiple Coverings of The Hamming Space

G. J.M. van Wee; G. D. Cohen; S. N. Litsyn

doi:10.1109/18.79931

A Note on Perfect Multiple Coverings of The Hamming Space

G. J.M. van Wee, G. D. Cohen, S. N. Litsyn

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10 Scopus citations

Abstract

Let Q be an alphabet of size q ≥ 2. The Hamming space Qⁿthat consists of all n-tuples of elements of Q is a metric space, provided with the Hamming distance function. a perfect multiple covering (PMC) is a code C in Qⁿsuch that there exist fixed numbers r and μ with the property that every word in Qⁿ is within distance r from exactly μ codewords of C. We give a few constructions of PMC's, and investigate in detail the problem of determining all possible parameters of PMC's with r =1.

Original language	English
Pages (from-to)	678-682
Number of pages	5
Journal	IEEE Transactions on Information Theory
Volume	37
Issue number	3
DOIs	https://doi.org/10.1109/18.79931
State	Published - May 1991
Externally published	Yes

Keywords

Multiple coverings
ball pool problems
covering radius
foot
perfect codes

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AB - Let Q be an alphabet of size q ≥ 2. The Hamming space Qnthat consists of all n-tuples of elements of Q is a metric space, provided with the Hamming distance function. a perfect multiple covering (PMC) is a code C in Qnsuch that there exist fixed numbers r and μ with the property that every word in Qn is within distance r from exactly μ codewords of C. We give a few constructions of PMC's, and investigate in detail the problem of determining all possible parameters of PMC's with r =1.

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KW - foot

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A Note on Perfect Multiple Coverings of The Hamming Space

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