Article ID Journal Published Year Pages File Type
4602376 Linear Algebra and its Applications 2008 12 Pages PDF
Abstract

Superregular matrices are a type of lower triangular Toeplitz matrix that arises in the context of constructing convolutional codes having a maximum distance profile. These matrices are characterized by the property that the only submatrices having a zero determinant are those whose determinants are trivially zero due to the lower triangular structure. In this paper, we discuss how superregular matrices may be used to construct codes having a maximum distance profile. We also present an upper bound on the minimum size a finite field must have in order that a superregular matrix of a given size can exist over that field. This, in turn, gives an upper bound on the smallest field size over which an MDP (n,k,δ) convolutional code can exist.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory