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On the Exact Lower Bounds of Encoding Circuit Sizes of Hamming Codes and Hadamard Codes

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Zhengrui Li, Sian-Jheng Lin, Yunghsiang S. Han

Information Theory · Submitted 26 Apr 2018

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

The authors' main claim To begin with, we prove the exact lower bound of circuit size required in the encoding of (punctured)~Hadamard codes and (extended)~Hamming codes.

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arXiv ID1804.09903 (version 2)
Pith IDCLANHDY6, Pith's permanent record of this paper and its review
CitationSian-Jheng Lin, Yunghsiang S. Han, Zhengrui Li. "On the Exact Lower Bounds of Encoding Circuit Sizes of Hamming Codes and Hadamard Codes." arXiv:1804.09903 (2018). https://pith.science/paper/CLANHDY6
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,543 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.48 · compares with prior results 0.07 · mentions code or data availability 0.03.

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

In this paper, we investigate the encoding circuit size of Hamming codes and Hadamard codes. To begin with, we prove the exact lower bound of circuit size required in the encoding of (punctured)~Hadamard codes and (extended)~Hamming codes. Then the encoding algorithms for (punctured)~Hadamard codes are presented to achieve the derived lower bounds. For (extended)~Hamming codes, we also propose encoding algorithms that achieve the lower bounds.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this paper, we investigate the encoding circuit size of Hamming codes and Hadamard codes. contribution 0.58 0.66 0.04 asserted 0.70
s1 To begin with, we prove the exact lower bound of circuit size required in the encoding of (punctured)~Hadamard codes and (extended)~Hamming codes. result 0.70 0.96 0.75 asserted 1.00
s2 Then the encoding algorithms for (punctured)~Hadamard codes are presented to achieve the derived lower bounds. contribution 0.53 0.93 0.14 asserted 1.00
s3 For (extended)~Hamming codes, we also propose encoding algorithms that achieve the lower bounds. contribution 0.74 0.95 0.19 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · 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

In this paper, we investigate the encoding circuit size of Hamming codes and Hadamard codes. To begin with, we prove the exact lower bound of circuit size required in the encoding of (punctured)~Hadamard codes and (extended)~Hamming codes. Then the encoding algorithms for (punctured)~Hadamard codes are presented to achieve the derived lower bounds. For (extended)~Hamming codes, we also propose encoding algorithms that achieve the lower bounds.

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