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.
- Error correcting code
- Hamiltonian cycle
- Nonadaptive group testing
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics