Entry-faithful 2-neighbour transitive codes

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چکیده

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Entry-faithful 2-neighbour transitive codes

We consider a code to be a subset of the vertex set of a Hamming graph. The set of s-neighbours of a code is the set of vertices, not in the code, at distance s from some codeword, but not distance less than s from any codeword. A 2-neighbour transitive code is a code which admits a group X of automorphisms which is transitive on the s-neighbours, for s = 1, 2, and transitive on the code itself...

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The Johnson graph J(v, k) has, as vertices, the k-subsets of a v-set V and as edges the pairs of k-subsets with intersection of size k − 1. We introduce the notion of a neighbour-transitive code in J(v, k). This is a vertex subset Γ such that the subgroup G of graph automorphisms leaving Γ invariant is transitive on both the set Γ of ‘codewords’ and also the set of ‘neighbours’ of Γ, which are ...

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Neighbour transitivity on codes in Hamming graphs

We consider a code to be a subset of the vertex set of a Hamming graph. In this setting a neighbour of the code is a vertex which differs in exactly one entry from some codeword. This paper examines codes with the property that some group of automorphisms acts transitively on the set of neighbours of the code. We call these codes neighbour transitive. We obtain sufficient conditions for a neigh...

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ژورنال

عنوان ژورنال: Designs, Codes and Cryptography

سال: 2015

ISSN: 0925-1022,1573-7586

DOI: 10.1007/s10623-015-0069-3