Families of nested completely regular codes and distance-regular graphs
In this paper infinite families of linear binary nested completely regular codes are constructed. They have covering radius ρ equal to 3 or 4, and are 1/2 i th parts, for i ∈ {1, ... , u} of binary (respectively, extended binary) Hamming codes of length n = 2 m - 1 (respectively, 2 m ), where m = 2u...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:142862 |
| Acceso en línea: | https://ddd.uab.cat/record/142862 https://dx.doi.org/urn:doi:10.3934/amc.2015.9.233 |
| Access Level: | acceso abierto |
| Palabra clave: | Completely regular codes Completely transitive codes Distance-regular graphs Distance-transitive graphs |
| Sumario: | In this paper infinite families of linear binary nested completely regular codes are constructed. They have covering radius ρ equal to 3 or 4, and are 1/2 i th parts, for i ∈ {1, ... , u} of binary (respectively, extended binary) Hamming codes of length n = 2 m - 1 (respectively, 2 m ), where m = 2u. In the usual way, i.e., as coset graphs, infinite families of embedded distance-regular coset graphs of diameter D equal to 3 or 4 are constructed. In some cases, the constructed codes are also completely transitive codes and the corresponding coset graphs are distance-transitive. This gives antipodal covers of some distance-regular and distance-transitive graphs. |
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