He Huang, Binzhou Xia, Sanming Zhou
Published 2016-09-13Version 1
We study perfect codes and related objects such as total perfect codes and perfect $t$-codes in Cayley graphs from the viewpoint of group rings. We give a uniform approach to such objects that enables us to obtain new results as well as generalizations of a few known results. In particular, we obtain conditions for a normal subgroup of a finite group to be a perfect code in some Cayley graph of the group. We also discuss related group-theoretic aspects of this approach and pose three open problems.
Perfect sets in Cayley graphs
A note on a Cayley graph of S_n
On the Cayley graph of a commutative ring with respect to its zero-divisors
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