Abstract
Abstract 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 (4 l −1)/3 .
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