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...

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Detalles Bibliográficos
Autores: Rifà i Coma, Josep|||0000-0001-9199-4001, Zinoviev, Victor|||0000-0002-7639-6115
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
Descripción
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.