On duals and parity-checks of convolutional codes over Z p r
A convolutional code C over Z_{p^r}((D)) is a Z_{p^r}((D))-submodule of Z_{p^r}^n((D)) that admits a polynomial set of generators, where Z_{p^r}((D)) stands for the ring of (semi-infinity) Laurent series. In this paper we study several structural properties of its dual C^{\perp} . We use these resul...
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| Other Authors: | , , |
| Format: | article |
| Language: | eng |
| Published: |
2019
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| Subjects: | |
| Online Access: | http://hdl.handle.net/10773/25975 |
| Country: | Portugal |
| Oai: | oai:ria.ua.pt:10773/25975 |
| Summary: | A convolutional code C over Z_{p^r}((D)) is a Z_{p^r}((D))-submodule of Z_{p^r}^n((D)) that admits a polynomial set of generators, where Z_{p^r}((D)) stands for the ring of (semi-infinity) Laurent series. In this paper we study several structural properties of its dual C^{\perp} . We use these results to provide a constructive algorithm to build an explicit generator matrix of C^{\perp}. Moreover, we show that the transpose of such a matrix is a parity-check matrix (also called syndrome former) of C. |
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