Constructing 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.