Dominated error correcting codes with distance two

Feliú Sagols, Laura P. Riccio, Charles Colbourn

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)294-302
Number of pages9
JournalJournal of Combinatorial Designs
Volume10
Issue number5
DOIs
StatePublished - Dec 1 2002

Keywords

  • Error correcting code
  • Hamiltonian cycle
  • Nonadaptive group testing

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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