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Additive perfect codes in Doob graphs
[article]
2018
arXiv
pre-print
The Doob graph D(m,n) is the Cartesian product of m>0 copies of the Shrikhande graph and n copies of the complete graph of order 4. Naturally, D(m,n) can be represented as a Cayley graph on the additive group (Z_4^2)^m × (Z_2^2)^n'× Z_4^n", where n'+n"=n. A set of vertices of D(m,n) is called an additive code if it forms a subgroup of this group. We construct a 3-parameter class of additive perfect codes in Doob graphs and show that the known necessary conditions of the existence of additive
arXiv:1806.04834v1
fatcat:7x4irnpribfzpg45epvezvjkde