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Weight Spectrum of Quasi-Perfect Binary Codes with Distance 4

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Valentine B. Afanassiev, Alexander A. Davydov

Information Theory · Submitted 12 Mar 2017

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

The authors' main claim We give exact recursive formulas for the weight spectrum of quasi-perfect codes and their dual codes.

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arXiv ID1703.04106 (version 2)
Pith IDODFVX2WT, Pith's permanent record of this paper and its review
CitationAlexander A. Davydov, Valentine B. Afanassiev. "Weight Spectrum of Quasi-Perfect Binary Codes with Distance 4." arXiv:1703.04106 (2017). https://pith.science/paper/ODFVX2WT
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,163 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.67 · compares with prior results 0.52 · mentions code or data availability 0.02.

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arXiv listing abstract v2. Results and the main claim are underlined; .

We consider the weight spectrum of a class of quasi-perfect binary linear codes with code distance 4. For example, extended Hamming code and Panchenko code are the known members of this class. Also, it is known that in many cases Panchenko code has the minimal number of weight 4 codewords. We give exact recursive formulas for the weight spectrum of quasi-perfect codes and their dual codes. As an example of application of the weight spectrum we derive a lower estimate for the conditional probability of correction of erasure patterns of high weights (equal to or greater than code distance).

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We consider the weight spectrum of a class of quasi-perfect binary linear codes with code distance 4. contribution 0.76 0.56 0.09 asserted 0.74
s1 For example, extended Hamming code and Panchenko code are the known members of this class. background 1.00 0.04 0.03 asserted 1.00
s2 Also, it is known that in many cases Panchenko code has the minimal number of weight 4 codewords. background 1.00 0.04 0.05 asserted 0.88
s3 We give exact recursive formulas for the weight spectrum of quasi-perfect codes and their dual codes. contribution 0.83 0.95 0.59 asserted 1.00
s4 As an example of application of the weight spectrum we derive a lower estimate for the conditional probability of correction of erasure patterns of high weights (equal to or greater than code distance). result 0.79 0.94 0.22 asserted 1.00

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

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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

We consider the weight spectrum of a class of quasi-perfect binary linear codes with code distance 4. For example, extended Hamming code and Panchenko code are the known members of this class. Also, it is known that in many cases Panchenko code has the minimal number of weight 4 codewords. We give exact recursive formulas for the weight spectrum of quasi-perfect codes and their dual codes. As an example of application of the weight spectrum we derive a lower estimate for the conditional probability of correction of erasure patterns of high weights (equal to or greater than code distance).

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