Naslov
Alphabet-almost-simple 2-neighbour-transitive codes

Autori
Gillespie, Neil ; Hawtin, Daniel

Izvornik
ARS Mathematica Contemporanea (1855-3966) 14 (2017), 2; 345-357

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
2-neighbour-transitive ; alphabet-almost-simple ; automorphism groups

Sažetak
Let X be a subgroup of the full automorphism group of the Hamming graph H(m, q), and C a subset of the vertices of the Hamming graph. We say that C is an (X, 2)-neighbour- transitive code if X is transitive on C, as well as C1 and C2, the sets of vertices which are distance 1 and 2 from the code. It has been shown that, given an (X, 2)-neighbour-transitive code C, there exists a subgroup of X with a 2-transitive action on the alphabet ; this action is thus almost-simple or affine. This paper completes the classification of (X, 2)-neighbour- transitive codes, with minimum distance at least 5, where the subgroup of X stabilising some entry has an almost-simple action on the alphabet in the stabilised entry. The main result of this paper states that the class of (X, 2) neighbour-transitive codes with an almost- simple action on the alphabet and minimum distance at least 3 consists of one infinite family of well known codes.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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