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New descriptions of the weighted Reed-Muller codes and the homogeneous Reed-Muller codes

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Harinaivo Andriatahiny, Vololona Harinoro Rakotomalala

Information Theory · Submitted 4 Jan 2017

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

The authors' main claim We give a description of the weighted Reed-Muller codes over a prime field in a modular algebra.

how it is stated · asserted 1.00 read the record →

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arXiv ID1701.01059 (version 1)
Pith IDGHRNVFBC, Pith's permanent record of this paper and its review
CitationHarinaivo Andriatahiny, Vololona Harinoro Rakotomalala. "New descriptions of the weighted Reed-Muller codes and the homogeneous Reed-Muller codes." arXiv:1701.01059 (2017). https://pith.science/paper/GHRNVFBC
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,827 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.26 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.09 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We give a description of the weighted Reed-Muller codes over a prime field in a modular algebra. A description of the homogeneous Reed-Muller codes in the same ambient space is presented for the binary case. A decoding procedure using the Landrock-Manz method is developed.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We give a description of the weighted Reed-Muller codes over a prime field in a modular algebra. contribution 1.00 0.94 0.32 asserted 1.00
s1 A description of the homogeneous Reed-Muller codes in the same ambient space is presented for the binary case. contribution 1.00 0.88 0.14 asserted 1.00
s2 A decoding procedure using the Landrock-Manz method is developed. method 0.72 0.92 0.17 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.68 · evidence from proof or derivation 1.00.

What was examined, and what was not

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not examined
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  • figures and tables
  • references and citing sentences
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  • P abstract
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  • T body sentences
  • C citations
  • R cross-paper relations

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

We give a description of the weighted Reed-Muller codes over a prime field in a modular algebra. A description of the homogeneous Reed-Muller codes in the same ambient space is presented for the binary case. A decoding procedure using the Landrock-Manz method is developed.

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