On hadamard full propelinear codes with associated group C2t × C2

We introduce the Hadamard full propelinear codes that factorize as direct product of groups such that their associated group is C2t × C2. We study the rank, the dimension of the kernel, and the structure of these codes. For several specific parameters we establish some links from circulant Hada-mard...

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Detalles Bibliográficos
Autores: Bailera, Ivan|||0000-0001-6772-4802, Borges, Joaquim|||0000-0002-5774-4874, Rifà i Coma, Josep|||0000-0001-9199-4001
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:307004
Acceso en línea:https://ddd.uab.cat/record/307004
https://dx.doi.org/urn:doi:10.3934/amc.2020041
Access Level:acceso abierto
Palabra clave:Hadamard full propelinear codes
Hadamard matrices
Kernel
Rank
Descripción
Sumario:We introduce the Hadamard full propelinear codes that factorize as direct product of groups such that their associated group is C2t × C2. We study the rank, the dimension of the kernel, and the structure of these codes. For several specific parameters we establish some links from circulant Hada-mard matrices and the nonexistence of the codes we study. We prove that the dimension of the kernel of these codes is bounded by 3 if the code is nonlinear. We also get an equivalence between circulant complex Hadamard matrix and a type of Hadamard full propelinear code, and we find a new example of circulant complex Hadamard matrix of order 16.