A new class of superregular matrices and MDP convolutional codes

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 sufficiently large finite field F$\mathbb{F}$. Such construction works for any given choice of characteristic of the field F$\mathbb{F}$ and code parameters (n,k,δ)$(n,k,\delta )$ such that (n−k)|δ$(n-k)|\delta$. We also discuss the size of F$\mathbb{F}$ needed so that the proposed matrices are superregular.