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...
| Autores: | , |
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| Formato: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2021 |
| País: | España |
| Recursos: | Universidad de León |
| Repositorio: | BULERIA. Repositorio Institucional de la Universidad de León |
| OAI Identifier: | oai:buleria.unileon.es:10612/26603 |
| Acesso em linha: | https://hdl.handle.net/10612/26603 |
| Access Level: | acceso abierto |
| Palavra-chave: | Matemáticas Convolutional codes Maximum Distance Profile Finite fields Goppa codes 12 Matemáticas |
| Resumo: | [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. |
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