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

Eindhoven University of Technology
Ecl. Natl. Sup. des Telecom.
Perm Agricultural Institute, Department of Cybernetics

Research output: Contribution to journal › Article › peer-review

11 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

Access to Document

10.1109/18.79931

Cite this

@article{06b0299d85534f8f9df4f364a4aed3d8,

title = "A Note on Perfect Multiple Coverings of The Hamming Space",

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.",

keywords = "Multiple coverings, ball pool problems, covering radius, foot, perfect codes",

author = "\{van Wee\}, \{G. J.M.\} and Cohen, \{G. D.\} and Litsyn, \{S. N.\}",

year = "1991",

month = may,

doi = "10.1109/18.79931",

language = "אנגלית",

volume = "37",

pages = "678--682",

journal = "IEEE Transactions on Information Theory",

issn = "0018-9448",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "3",

}

TY - JOUR

T1 - A Note on Perfect Multiple Coverings of The Hamming Space

AU - van Wee, G. J.M.

AU - Cohen, G. D.

AU - Litsyn, S. N.

PY - 1991/5

Y1 - 1991/5

N2 - 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.

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.

KW - Multiple coverings

KW - ball pool problems

KW - covering radius

KW - foot

KW - perfect codes

UR - https://www.scopus.com/pages/publications/0026156005

U2 - 10.1109/18.79931

DO - 10.1109/18.79931

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0026156005

SN - 0018-9448

VL - 37

SP - 678

EP - 682

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 3

ER -

A Note on Perfect Multiple Coverings of The Hamming Space

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this