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Constructions of MDS convolutional codes using superregular matrices

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Julia Lieb, Raquel Pinto

Information Theory · Submitted 26 Mar 2019

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this paper, we show that taking the constant matrix coefficients of a polynomial matrix as submatrices of a superregular matrix, we obtain a column reduced generator matrix of an MDS convolutional code with a certain rate and a certain degree.

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arXiv ID1903.10986 (version 3)
Pith IDM7BABSK7, Pith's permanent record of this paper and its review
CitationJulia Lieb, Raquel Pinto. "Constructions of MDS convolutional codes using superregular matrices." arXiv:1903.10986 (2019). https://pith.science/paper/M7BABSK7
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,982 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.10 · mentions code or data availability 0.02.

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arXiv listing abstract v3. Results and the main claim are underlined; .

Maximum distance separable convolutional codes are the codes that present best performance in error correction among all convolutional codes with certain rate and degree. In this paper, we show that taking the constant matrix coefficients of a polynomial matrix as submatrices of a superregular matrix, we obtain a column reduced generator matrix of an MDS convolutional code with a certain rate and a certain degree. We then present two novel constructions that fulfill these conditions by considering two types of superregular matrices.

background contribution method result interpretation main claim

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 Maximum distance separable convolutional codes are the codes that present best performance in error correction among all convolutional codes with certain rate and degree. background 1.00 0.04 0.03 asserted 1.00
s1 In this paper, we show that taking the constant matrix coefficients of a polynomial matrix as submatrices of a superregular matrix, we obtain a column reduced generator matrix of an MDS convolutional code with a certain rate and a certain degree. contribution 0.55 0.95 0.84 asserted 1.00
s2 We then present two novel constructions that fulfill these conditions by considering two types of superregular matrices. contribution 0.96 0.95 0.21 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.58 · evidence from proof or derivation 0.99.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Maximum distance separable convolutional codes are the codes that present best performance in error correction among all convolutional codes with certain rate and degree. In this paper, we show that taking the constant matrix coefficients of a polynomial matrix as submatrices of a superregular matrix, we obtain a column reduced generator matrix of an MDS convolutional code with a certain rate and a certain degree. We then present two novel constructions that fulfill these conditions by considering two types of superregular matrices.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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  • Theorem 3.2 of [ref] provides a construction for MDP convolutional codes where the required field size is smaller than the field size in [ref] .

    Complete MDP convolutional codes · Comparison of constructions for MDS convolutional codes · 1.00

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