Conway Groupoids and Completely Transitive Codes
نویسندگان
چکیده
منابع مشابه
Families of completely transitive codes and distance transitive graphs
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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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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Completely transitive codes were introduced by P. Solé as a special case of binary linear completely regular codes. The existence of such codes is closely related to the existence of certain permutation groups. The nonexistence of highly transitive permutation groups allows us to prove the nonexistence of completely transitive codes with error-correcting capability greater than 4.
متن کاملA family of binary completely transitive codes and distance-transitive graphs
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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ژورنال
عنوان ژورنال: Combinatorica
سال: 2017
ISSN: 0209-9683,1439-6912
DOI: 10.1007/s00493-016-3433-7