On the existence and construction of maximum distance profile convolutional codes

[EN] In this paper, we study the conditions for a convolutional code to be MDP in terms of the size of the base field Fq as well as the openness of the MDP property in a given family of convolutional codes. Given (n; k; ), our main result is an explicit bound depending on (n; k; ) such that if q is...

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Detalles Bibliográficos
Autores: Muñoz Castañeda, Ángel Luis, Plaza Martín, Francisco J.
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2021
País:España
Institución:Universidad de León
Repositorio:BULERIA. Repositorio Institucional de la Universidad de León
OAI Identifier:oai:buleria.unileon.es:10612/26603
Acceso en línea:https://hdl.handle.net/10612/26603
Access Level:acceso abierto
Palabra clave:Matemáticas
Convolutional codes
Maximum Distance Profile
Finite fields
Goppa codes
12 Matemáticas
Descripción
Sumario:[EN] In this paper, we study the conditions for a convolutional code to be MDP in terms of the size of the base field Fq as well as the openness of the MDP property in a given family of convolutional codes. Given (n; k; ), our main result is an explicit bound depending on (n; k; ) such that if q is greater than this bound, there exists a (n; k; ) MDP convolutional code. A similar result is also o ered for complete MDP convolutional codes. We show that these bounds are much lower than that those appeared so far in the literature. Finally, we show an explicit and simple construction procedure for MDP convolutional Goppa codes of dimension one.