Perfect Codes in Antipodal Distance-Transitive Graphs.
نویسندگان
چکیده
منابع مشابه
Antipodal Distance Transitive Covers of Complete Graphs
This paper is a contribution towards the determination of all finite distance-transitive graphs. We obtain a classification of all the antipodal distance-transitive graphs having as antipodal quotient a complete graph Kn . Such a graph necessarily has diameter 2 or 3 (see for example [2, Proposition 4.2.2 (ii)]). Those of diameter 2 are simply the complete multipartite graphs Kr,...,r with n pa...
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In a previous work, the authors found new families of linear binary completely regular codes with the covering radius ρ = 3 and ρ = 4. In this paper, the automorphism groups of such codes are computed and it is proven that the codes are not only completely regular, but also completely transitive. From these completely transitive codes, in the usual way, i.e., as coset graphs, new presentations ...
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In this paper new infinite families of linear binary completely transitive codes are presented. They have covering radius ρ = 3 and 4, and are a half part of the binary Hamming and the binary extended Hamming code of length n = 2 − 1 and 2, respectively, where m is even. From these new completely transitive codes, in the usual way, i.e., as coset graphs, new presentations of infinite families o...
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Cameron's proof of this result is based on Sims' Conjecture, which has only been shown to hold using the classification of finite simple groups. In the final section of [1], Cameron indicates how Theorem 1 might be proved in an elementary fashion using Macpherson's classification of infinite distance-transitive graphs of finite valency [4]. Corollary 1 below provides the missing portion of this...
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ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 1974
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-11532