On Perfect Codes in the Johnson Graph

Published 29 Apr 2010 in cs.IT and math.IT | (1004.5195v1)

Abstract: In this paper we consider the existence of nontrivial perfect codes in the Johnson graph J(n,w). We present combinatorial and number theory techniques to provide necessary conditions for existence of such codes and reduce the range of parameters in which 1-perfect and 2-perfect codes may exist.

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