Completely Transitive Codes in Hamming Graphs
نویسندگان
چکیده
منابع مشابه
Completely Transitive Codes in Hamming Graphs
A code in a graph 0 is a non-empty subset C of the vertex set V of 0. Given C , the partition of V according to the distance of the vertices away from C is called the distance partition of C . A completely regular code is a code whose distance partition has a certain regularity property. A special class of completely regular codes are the completely transitive codes. These are completely regula...
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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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In this paper we construct new family of binary linear completely transitive (and, therefore, completely regular) codes. The covering radius of these codes is growing with the length of the code. In particular, for any integer ρ ≥ 2, there exist two codes in the constructed class of codes with d = 3, covering radius ρ and length ( 4 ρ 2 ) and ( 4 ρ+2 2 ) , respectively. These new completely tra...
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We consider a code to be a subset of the vertex set of a Hamming graph. We examine elusive pairs, code-group pairs where the code is not determined by knowledge of its set of neighbours. We construct a new infinite family of elusive pairs, where the group in question acts transitively on the set of neighbours of the code. In our examples, we find that the alphabet size always divides the length...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 1999
ISSN: 0195-6698
DOI: 10.1006/eujc.1999.0313