# Constructions of MDS convolutional codes using superregular matrices

## TL;DR

This paper introduces new methods for constructing MDS convolutional codes using superregular matrices, enhancing error correction capabilities with novel algebraic techniques.

## Contribution

It presents two new constructions of MDS convolutional codes based on superregular matrices, expanding the algebraic tools for code design.

## Key findings

- Constructed MDS convolutional codes with optimal error correction.
- Demonstrated the effectiveness of superregular matrices in code construction.
- Provided explicit algebraic methods for code design.

## 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.