A code is a subset of the vertex set of a Hamming graph. The set of s-neighbours of a code is the set of all vertices at Hamming distance s from their nearest codeword. A code C is s-elusive if there exists a distinct code that is equivalent to ...
In a previous work, the authors found new families of linear binary completely regular codes with covering radius , where { 3 , 4 } . In this paper, the automorphism groups of such codes are computed and it is proven that the codes are not only ...
The Johnson graph $$J(v,k)$$ J ( v , k ) has, as vertices, the $$k$$ k -subsets of a $$v$$ v -set $$\mathcal {V}$$ V and as edges the pairs of $$k$$ k -subsets with intersection of size $$k-1$$ k - 1 . We introduce the notion of a neighbour-transitive code in $$J(v,k)$$ J ( v , k ) . This is a proper vertex subset $$\Gamma $$ Γ such that the subgroup $$G$$ G of graph ...
Kluwer Academic Publishers
United States
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