Superregular matrices and applications to convolutional codes

DOI10.1016/j.laa.2016.02.034zbMath1391.94851arXiv1601.02960OpenAlexW2963992030MaRDI QIDQ269520

P. J. Almeida, Raquel Pinto, D. Napp Avelli

Publication date: 18 April 2016

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.02960

zbMATH Keywords

convolutional codeoptimal codesuperregular matrixforney indices

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Convolutional codes (94B10) Toeplitz, Cauchy, and related matrices (15B05)

Related Items (18)

Constructing strongly-MDS convolutional codes with maximum distance profile ⋮ On Optimal Extended Row Distance Profile ⋮ Constructions of MDS convolutional codes using superregular matrices ⋮ \(1/n\) turbo codes from linear system point of view ⋮ Systematic maximum sum rank codes ⋮ Convolutional codes over finite chain rings, MDP codes and their characterization ⋮ A decoding algorithm for 2D convolutional codes over the erasure channel ⋮ Weighted Reed–Solomon convolutional codes ⋮ MDS 2D convolutional codes with optimal 1D horizontal projections ⋮ Concatenation of convolutional codes and rank metric codes for multi-shot network coding ⋮ Construction of systematic \((k+1,k)\) memory MDS sliding window codes over embedded fields ⋮ Series concatenation of 2D convolutional codes by means of input-state-output representations ⋮ Complete MDP convolutional codes ⋮ A new rank metric for convolutional codes ⋮ Erasure decoding of convolutional codes using first-order representations ⋮ Serial concatenation of a block code and a 2D convolutional code ⋮ Block Toeplitz matrices for burst-correcting convolutional codes ⋮ Necessary field size and probability for MDP and complete MDP convolutional codes

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• On MDS codes via Cauchy matrices
• Strongly-MDS convolutional codes
• On generator matrices of MDS codes (Corresp.)
• Constructions of MDS-convolutional codes
• Totally positive matrices

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