Dominated error correcting codes with distance two

Feliú Sagols; Laura P. Riccio; Charles Colbourn

doi:10.1002/jcd.10012

Dominated error correcting codes with distance two

Feliú Sagols, Laura P. Riccio, Charles Colbourn

Computer Science and Engineering

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

5 Scopus citations

Abstract

We study the hamiltonicity of certain graphs obtained from the hypercube as a means of producing a binary code of distance two and length n, whose codewords are ordered so that for each two consecutive codewords, one dominates the other. One vector dominates the other, if and only if, in all the positions where one of them has a zero, the other has a zero too. These dominated codes have applications in group testing for consecutive defectives. We also determine when the vectors can be ordered so that every two consecutive vectors have the domination property, and are at distance two; this is a natural generalization of Gray codes.

Original language	English (US)
Pages (from-to)	294-302
Number of pages	9
Journal	Journal of Combinatorial Designs
Volume	10
Issue number	5
DOIs	https://doi.org/10.1002/jcd.10012
State	Published - Dec 1 2002

Keywords

Error correcting code
Hamiltonian cycle
Nonadaptive group testing

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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10.1002/jcd.10012

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author = "Feli{\'u} Sagols and Riccio, {Laura P.} and Charles Colbourn",

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AU - Riccio, Laura P.

AU - Colbourn, Charles

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N2 - We study the hamiltonicity of certain graphs obtained from the hypercube as a means of producing a binary code of distance two and length n, whose codewords are ordered so that for each two consecutive codewords, one dominates the other. One vector dominates the other, if and only if, in all the positions where one of them has a zero, the other has a zero too. These dominated codes have applications in group testing for consecutive defectives. We also determine when the vectors can be ordered so that every two consecutive vectors have the domination property, and are at distance two; this is a natural generalization of Gray codes.

AB - We study the hamiltonicity of certain graphs obtained from the hypercube as a means of producing a binary code of distance two and length n, whose codewords are ordered so that for each two consecutive codewords, one dominates the other. One vector dominates the other, if and only if, in all the positions where one of them has a zero, the other has a zero too. These dominated codes have applications in group testing for consecutive defectives. We also determine when the vectors can be ordered so that every two consecutive vectors have the domination property, and are at distance two; this is a natural generalization of Gray codes.

KW - Error correcting code

KW - Hamiltonian cycle

KW - Nonadaptive group testing

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Dominated error correcting codes with distance two

Abstract

Keywords

ASJC Scopus subject areas

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