A new class of superregular matrices and MDP convolutional codes

TL;DR

This paper introduces a new class of superregular matrices over large finite fields, enabling the construction of MDP convolutional codes with desirable properties for any given code parameters.

Contribution

It presents a novel construction of superregular matrices applicable to a wide range of code parameters and field characteristics, expanding the toolkit for MDP convolutional code design.

Findings

Constructed superregular matrices over large finite fields.

Applicable to any code parameters with (n-k)|d.

Discussed field size requirements for superregularity.

Abstract

This paper deals with the problem of constructing superregular matrices that lead to MDP convolutional codes. These matrices are a type of lower block triangular Toeplitz matrices with the property that all the square submatrices that can possibly be nonsingular due to the lower block triangular structure are nonsingular. We present a new class of matrices that are superregular over a suficiently large finite field F. Such construction works for any given choice of characteristic of the field F and code parameters (n; k; d) such that (n-k)|d. Finally, we discuss the size of F needed so that the proposed matrices are superregular.