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The existence of perfect codes in Doob graphs

Published 9 Oct 2018 in cs.IT, cs.DM, math.CO, and math.IT | (1810.03772v2)

Abstract: We solve the problem of existence of perfect codes in the Doob graph. It is shown that 1-perfect codes in the Doob graph D(m,n) exist if and only if 6m+3n+1 is a power of 2; that is, if the size of a 1-ball divides the number of vertices. Keywords: perfect codes, distance-regular graphs, Doob graphs, Eisenstein-Jacobi integers.

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Authors (1)

  1. Denis S. Krotov 

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