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Perfect codes in graphs. (English) Zbl 0256.94009

Summary: The classical problem of the existence of perfect codes is set in a vector space. In this paper it is shown that the natural setting for the problem is the class of distance-transitive graphs. A general theory is developed that leads to a simple criterion for the existence of a perfect code in a distance-transitive graph, and it is shown that this criterion implies Lloyd’s theorem in the classical case.

MSC:

94B60 Other types of codes
05C90 Applications of graph theory
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References:

[1] Biggs, N. L., (Finite Groups of Automorphisms (1971), Cambridge Univ. Press: Cambridge Univ. Press London), (London Math. Society Lecture Notes, No. 6) · Zbl 0221.05049
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