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Superregular Matrices and the Construction of Convolutional Codes having a Maximum Distance Profile

R. Hutchinson·R. Smarandache·J. Trumpf
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Abstract

Superregular matrices are a class of lower triangular Toeplitz matrices that arise in the context of constructing convolutional codes having a maximum distance profile. These matrices are characterized by the property that no submatrix has a zero determinant unless it is 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 introduce group actions that preserve the superregularity property and 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.

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R. Hutchinson, R. Smarandache, J. Trumpf. 2006-07-19. Superregular Matrices and the Construction of Convolutional Codes having a Maximum Distance Profile. https://arxiv.org/abs/cs/0607089

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