Minimal binary 2-neighbour-transitive codes
| العنوان: | Minimal binary 2-neighbour-transitive codes |
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| المؤلفون: | Cheryl E. Praeger, Daniel R. Hawtin |
| المصدر: | Journal of Combinatorial Theory, Series A. 171:105173 |
| بيانات النشر: | Elsevier BV, 2020. |
| سنة النشر: | 2020 |
| مصطلحات موضوعية: | 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 |
| الوصف: | 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 |
| تدمد: | 0097-3165 |
| DOI: | 10.1016/j.jcta.2019.105173 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::11649cec0ffcb06e483322f243d27511 https://doi.org/10.1016/j.jcta.2019.105173 |
| Rights: | OPEN |
| رقم الانضمام: | edsair.doi.dedup.....11649cec0ffcb06e483322f243d27511 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 00973165 |
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| DOI: | 10.1016/j.jcta.2019.105173 |