Completely regular codes with different parameters giving the same distance-regular coset graphs
We construct several classes of completely regular codes with different parameters, but identical intersection array. Given a prime power q and any two natural numbers a,b, we construct completely transitive codes over different fields with covering radius ρ=min{a,b}ρ=min{a,b} and identical intersec...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:171453 |
| Acceso en línea: | https://ddd.uab.cat/record/171453 https://dx.doi.org/urn:doi:10.1016/j.disc.2017.03.001 |
| Access Level: | acceso abierto |
| Palabra clave: | Bilinear forms graph Completely regular code Completely transitive code Coset graph Distance-regular graph Distance-transitive graph Kronecker product construction Lifting of a field Uniformly packed code |
| Sumario: | We construct several classes of completely regular codes with different parameters, but identical intersection array. Given a prime power q and any two natural numbers a,b, we construct completely transitive codes over different fields with covering radius ρ=min{a,b}ρ=min{a,b} and identical intersection array, specifically, one code over F_q^r for each divisor r of a or b. As a corollary, for any prime power qq, we show that distance regular bilinear forms graphs can be obtained as coset graphs from several completely regular codes with different parameters. |
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