Constructions of MDS convolutional codes using superregular matrices

Year 2020, Volume: 7 Issue: 1 (Special Issue in Algebraic Coding Theory: New Trends and Its Connections), 73 - 84, 29.02.2020

Julia Lieb Raquel Pinto

https://doi.org/10.13069/jacodesmath.645029

Cited By: 6

Abstract

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.

Keywords

Convolutional codes, MDS codes, Superregular matrices

Supporting Institution

Funda\c{c}\~ao para a Ci\^encia e a Tecnologia (FCT)

Project Number

UID/MAT/04106/2019

Thanks

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.

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