Abstract
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. We give a classification of 2-neighbour transitive codes, with minimum distance δ≥5, for which X acts faithfully on the set of entries of the Hamming graph.
Original language | English |
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Pages (from-to) | 549-564 |
Number of pages | 16 |
Journal | Designs, Codes and Cryptography |
Volume | 79 |
Issue number | 3 |
Early online date | 2 Apr 2015 |
DOIs | |
Publication status | Published - 1 Jun 2016 |
Keywords
- Completely transitive codes
- Regular codes
- 2-Neighbour transitive codes
- Automorphisms groups
- Hamming graph