Minimal binary 2-neighbour-transitive codes
نویسندگان
چکیده
منابع مشابه
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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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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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2020
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2019.105173