On the State Approach Representations of Convolutional Codes over Rings of Modular Integers
[EN] In this study, we prove the existence of minimal first-order representations for convolutional codes with the predictable degree property over principal ideal artinian rings. Further, we prove that any such first-order representation leads to an input/state/output representation of the code pro...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| 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:10612/19442 |
| Acceso en línea: | https://www.mdpi.com/2227-7390/9/22/2962 https://hdl.handle.net/10612/19442 |
| Access Level: | acceso abierto |
| Palabra clave: | Matemáticas Convolutional codes Representations Rings of modular integers 1201.05 Campos, Anillos, Álgebras 1201.10 Álgebra Lineal |
| Sumario: | [EN] In this study, we prove the existence of minimal first-order representations for convolutional codes with the predictable degree property over principal ideal artinian rings. Further, we prove that any such first-order representation leads to an input/state/output representation of the code provided the base ring is local. When the base ring is a finite field, we recover the classical construction, studied in depth by J. Rosenthal and E. V. York. This allows us to construct observable convolutional codes over such rings in the same way as is carried out in classical convolutional coding theory. Furthermore, we prove the minimality of the obtained representations. This completes the study of the existence of input/state/output representations of convolutional codes over rings of modular integers. |
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