Minimal binary 2-neighbour-transitive codes
| Autor: | Cheryl E. Praeger, Daniel R. Hawtin |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Discrete mathematics
Class (set theory) Transitive relation 010102 general mathematics Structure (category theory) Binary number 0102 computer and information sciences Permutation group 01 natural sciences 2-Neighbour-transitive Completely transitive Completely regular Hamming graph Binary code 2-Transitive Theoretical Computer Science Permutation Computational Theory and Mathematics 010201 computation theory & mathematics FOS: Mathematics Mathematics - Combinatorics Discrete Mathematics and Combinatorics Combinatorics (math.CO) 0101 mathematics 05E18 94B25 51E05 20C05 Mathematics |
| Zdroj: | Journal of Combinatorial Theory, Series A. 171:105173 |
| ISSN: | 0097-3165 |
| Popis: | 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 $\mathbb{F}_2$ for finite $2$-transitive permutation groups. Comment: 17 pages. arXiv admin note: text overlap with arXiv:1806.10514 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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