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Title: On duals and parity-checks of convolutional codes over Z p r
Author: El Oued, Mohamed
Napp, Diego
Pinto, Raquel
Toste, Marisa
Keywords: Finite rings
Convolutional codes over finite rings
Dual codes
Matrix representations
Issue Date: Jan-2019
Publisher: Elsevier
Abstract: 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.
Peer review: yes
DOI: 10.1016/j.ffa.2018.08.012
ISSN: 1071-5797
Publisher Version:!
Appears in Collections:CIDMA - Artigos
SCG - Artigos

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