Minimal binary 2-neighbour-transitive codes (CROSBI ID 290793)
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Podaci o odgovornosti
Hawtin, Daniel ; Praeger, Cheryl
engleski
Minimal binary 2-neighbour-transitive codes
The main result here is a characterisation of binary 2-neighbour-transitive codes with minimum distance at least 5 via their minimal subcodes, which are found to be generated by certain designs. The motivation for studying this class of codes comes primarily from their relationship to the class of completely regular codes. The results contained here yield many more examples of 2-neighbour-transitive codes than previous classification results of families of 2-neighbour-transitive codes. In the process, new lower bounds on the minimum distance of particular sub-families are produced. Several results on the structure of 2-neighbour-transitive codes with arbitrary alphabet size are also proved. The proofs of the main results apply the classification of minimal and pre-minimal submodules of the permutation modules over F-2 for finite 2-transitive permutation groups.
2-Neighbour-transitive ; Completely transitive ; Completely regular ; Hamming graph ; Binary code ; 2-Transitive
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Podaci o izdanju
171
2020.
105173
19
objavljeno
0097-3165
1096-0899
10.1016/j.jcta.2019.105173