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Title: Superregular matrices and applications to convolutional codes
Author: Almeida, P. J.
Napp, D.
Pinto, R.
Keywords: Convolutional code
Forney indices
Optimal code
Superregular matrix
Issue Date: 15-Jun-2016
Publisher: Elsevier
Abstract: The main results of this paper are twofold: the first one is a matrix theoretical result. We say that a matrix is superregular if all of its minors that are not trivially zero are nonzero. Given a a×b, a ≥ b, superregular matrix over a field, we show that if all of its rows are nonzero then any linear combination of its columns, with nonzero coefficients, has at least a−b + 1 nonzero entries. Secondly, we make use of this result to construct convolutional codes that attain the maximum possible distance for some fixed parameters of the code, namely, the rate and the Forney indices. These results answer some open questions on distances and constructions of convolutional codes posted in the literature.
Peer review: yes
DOI: 10.1016/j.laa.2016.02.034
ISSN: 0024-3795
Appears in Collections:CIDMA - Artigos
AGG - Artigos

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