Sporadic neighbour-transitive codes in Johnson graphs
نویسندگان
چکیده
منابع مشابه
Sporadic neighbour-transitive codes in Johnson graphs
We classify the neighbour-transitive codes in Johnson graphs J(v, k) of minimum distance at least 3 which admit a neighbour-transitive group of automorphisms that is an almost simple 2-transitive group of degree v and does not occur in an infinite family of 2-transitive groups. The result of this classification is a table of 22 codes with these properties. Many have relatively large minimum dis...
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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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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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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: 2013
ISSN: 0925-1022,1573-7586
DOI: 10.1007/s10623-013-9853-0