Doob graphs are distance-regular graphs having the same parameters as the quaternary Hamming graphs. Delsarte's generalization of Lloyd's theorem implies that a tight 2e-design or a perfect e-code in a Doob graph can possibly exist only when e=1. We construct perfect 1-codes in Doob graphs of diameter 5, and tight 2-designs in all Doob graphs of diameter (4l-1)/3.
|Number of pages||9|
|Journal||Journal of Statistical Planning and Inference|
|Publication status||Published - 2000 May 1|
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics