Superregular Matrices and the Construction of Convolutional Codes having a Maximum Distance Profile
<|reference_start|>Superregular Matrices and the Construction of Convolutional Codes having a Maximum Distance Profile: 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.<|reference_end|>
@article{hutchinson2006superregular,
    title={Superregular Matrices and the Construction of Convolutional Codes having
  a Maximum Distance Profile},
    author={R. Hutchinson, R. Smarandache, J. Trumpf},
    journal={arXiv preprint arXiv:cs/0607089},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0607089},
    primaryClass={cs.IT math.CO math.IT}
}