Constructing Superregular Matrices

TL;DR

This paper introduces new methods for constructing superregular matrices, which are matrices with all square submatrices non-singular, crucial for applications in communications.

Contribution

It proposes a novel construction of block superregular matrices using Kronecker products and smaller superregular matrices over smaller fields.

Findings

New construction method using Kronecker product.

Two constructions via smaller superregular matrices.

Enhanced tools for designing superregular matrices.

Abstract

Superregular matrices, i.e., matrices where all square submatrices are non-singular, have a wide range of applications in communications. A superregular block matrix is a broader concept where all full block submatrices, with the appropriate size, are non-singular. In this work we propose a construction of block superregular matrices based on the Kronecker product of superregular matrices with non-singular matrices. Furthermore, we propose two constructions of superregular matrices via other smaller superregular matrices over smaller fields.