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## Constructions of MDS convolutional codes using superregular matrices

#### Julia LİEB [1] , Raquel PİNTO [2]

Maximum distance separable convolutional codes are the codes that present best performance in error correction among all convolutional codes with certain rate and degree. In this paper, we show that taking the constant matrix coefficients of a polynomial matrix as submatrices of a superregular matrix, we obtain a column reduced generator matrix of an MDS convolutional code with a certain rate and a certain degree. We then present two novel constructions that fulfill these conditions by considering two types of superregular matrices.
Convolutional codes, MDS codes, Superregular matrices
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Primary Language en Engineering Articles Orcid: 0000-0003-4211-1596Author: Julia LİEB (Primary Author) Orcid: 0000-0002-8168-4023Author: Raquel PİNTO Funda\c{c}\~ao para a Ci\^encia e a Tecnologia (FCT) UID/MAT/04106/2019 This work was supported by Funda\c{c}\~ao para a Ci\^encia e a Tecnologia (FCT) within project UID/MAT/04106/2019 (CIDMA) and the German Research Foundation (DFG) within grant LI3103/1-1. Publication Date : February 29, 2020
 Bibtex @research article { jacodesmath645029, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {}, publisher = {Yildiz Technical University}, year = {2020}, volume = {7}, pages = {73 - 84}, doi = {10.13069/jacodesmath.645029}, title = {Constructions of MDS convolutional codes using superregular matrices}, key = {cite}, author = {Li̇eb, Julia and Pi̇nto, Raquel} } APA Li̇eb, J , Pi̇nto, R . (2020). Constructions of MDS convolutional codes using superregular matrices . Journal of Algebra Combinatorics Discrete Structures and Applications , 7 (1) , 73-84 . DOI: 10.13069/jacodesmath.645029 MLA Li̇eb, J , Pi̇nto, R . "Constructions of MDS convolutional codes using superregular matrices" . Journal of Algebra Combinatorics Discrete Structures and Applications 7 (2020 ): 73-84 Chicago Li̇eb, J , Pi̇nto, R . "Constructions of MDS convolutional codes using superregular matrices". Journal of Algebra Combinatorics Discrete Structures and Applications 7 (2020 ): 73-84 RIS TY - JOUR T1 - Constructions of MDS convolutional codes using superregular matrices AU - Julia Li̇eb , Raquel Pi̇nto Y1 - 2020 PY - 2020 N1 - doi: 10.13069/jacodesmath.645029 DO - 10.13069/jacodesmath.645029 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 73 EP - 84 VL - 7 IS - 1 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.645029 UR - https://doi.org/10.13069/jacodesmath.645029 Y2 - 2019 ER - EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications Constructions of MDS convolutional codes using superregular matrices %A Julia Li̇eb , Raquel Pi̇nto %T Constructions of MDS convolutional codes using superregular matrices %D 2020 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 7 %N 1 %R doi: 10.13069/jacodesmath.645029 %U 10.13069/jacodesmath.645029 ISNAD Li̇eb, Julia , Pi̇nto, Raquel . "Constructions of MDS convolutional codes using superregular matrices". Journal of Algebra Combinatorics Discrete Structures and Applications 7 / 1 (February 2020): 73-84 . https://doi.org/10.13069/jacodesmath.645029 AMA Li̇eb J , Pi̇nto R . Constructions of MDS convolutional codes using superregular matrices. Journal of Algebra Combinatorics Discrete Structures and Applications. 2020; 7(1): 73-84. Vancouver Li̇eb J , Pi̇nto R . Constructions of MDS convolutional codes using superregular matrices. Journal of Algebra Combinatorics Discrete Structures and Applications. 2020; 7(1): 73-84.

Authors of the Article
[1]
[2]