$c^3$-Locally Testable Codes from Lossless Expanders

Min-Hsiu Hsieh; Ting-Chun Lin

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$c^3$-Locally Testable Codes from Lossless Expanders

Ting-Chun Lin, Min-Hsiu Hsieh

Information Theory · Submitted 27 Jan 2022

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

The authors' main claim In this work, we construct a new LTC family using 1-sided lossless expanders and balanced products.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,555 input tokens.

What the abstract itself states, as probabilities: claims first 0.12 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.02 · states quantitative result 0.30 · compares with prior results 0.20 · mentions code or data availability 0.02.

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

A locally testable code (LTC) is an error correcting code with a property tester. The tester tests if a word is codeword by reading constant random bits and rejects the word with probability proportional to the distance from the word to the closest codeword. An important open question until recently is whether there exist $c^3$-LTCs which are LTCs with constant rate, constant relative distance and constant locality. In this work, we construct a new LTC family using 1-sided lossless expanders and balanced products.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	A locally testable code (LTC) is an error correcting code with a property tester.	background 1.00	0.03	0.02	asserted 1.00
s1	The tester tests if a word is codeword by reading constant random bits and rejects the word with probability proportional to the distance from the word to the closest codeword.	background 1.00	0.04	0.03	asserted 1.00
s2	An important open question until recently is whether there exist $c^3$-LTCs which are LTCs with constant rate, constant relative distance and constant locality.	gap 0.97	0.04	0.06	asserted 0.91
s3	In this work, we construct a new LTC family using 1-sided lossless expanders and balanced products.	contribution 0.93	0.96	0.81	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.72 · evidence from proof or derivation 1.00.

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arXiv listing abstract v2

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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

A locally testable code (LTC) is an error correcting code with a property tester. The tester tests if a word is codeword by reading constant random bits and rejects the word with probability proportional to the distance from the word to the closest codeword. An important open question until recently is whether there exist $c^3$-LTCs which are LTCs with constant rate, constant relative distance and constant locality. In this work, we construct a new LTC family using 1-sided lossless expanders and balanced products.

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References

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Full-Rank Constructions of Explicit Lossless Expanders and Good Small-Set qLTCs
quant-ph 2026-11 accept novelty 8.0 of 10

An explicit family of asymptotically good quantum LDPC codes with full-rank check matrices and linear-range small-set soundness, built from full-rank lossless expanders with free 2-group actions.
Good Quantum LDPC Codes with Linear Time Decoders
quant-ph 2022-06 conditional novelty 7.0 of 10

The authors build explicit quantum LDPC codes with constant rate and distance plus a linear-time decoder, and prove that random tensor codes have optimal robustness.
Quantum Tanner codes
quant-ph 2022-02 accept novelty 7.0 of 10

By placing qubits on the squares of a left-right Cayley complex and enforcing Tanner-code constraints at the vertices, the authors construct quantum LDPC codes with constant rate and minimum distance growing linearly ...

How the literature uses it

9 arXiv papers cite this in 26 sentences

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

Papers citing it · 18 sentences without a confident label

Uses its method or tool 3 papers

Our method relies on recent breakthroughs on LTCs [ref] and quantum LDPC codes [ref] .

Explicit Lower Bounds Against $\Omega(n)$-Rounds of Sum-of-Squares · Constructing SS-HDX · 0.88
Given a classical LTC [ref] , let $2^X(0) →2^X(1)$ be the parity-check matrix where $X(0)$ are the bits and $X(1)$ are the checks.

Geometrically Local Quantum and Classical Codes from Subdivision · Code Construction · 0.85
To reduce the qubit overhead for generating resource states, we propose using a double-constant classical LTC with constant encoding rate and constant soundness [ref] .

Accelerating Fault-Tolerant Quantum Computation with Good qLDPC Codes · Locally-testable state preparation · 0.89

Cites it as background 3 papers

Our work fits into a line of recent works on quantum LDPC codes and LTCs [ref] .

Good Quantum LDPC Codes with Linear Time Decoders · Related work · 0.96
<Ref> is based on a new form of high dimensional expansion (HDX), a nascent area of computer science and math that has already seen an impressive array of breakthrough results across areas such as coding theory [ref] , approximate sampling [ref] , approximation algorithms [ref] , analysis of boolean functions [ref] , agreement testing [ref] , and, recently, Sum-of-Squares lower bounds [ref] .

Explicit Lower Bounds Against $\Omega(n)$-Rounds of Sum-of-Squares · High Dimensional Small-Set Expanders · 0.96
These objects are applicable to various areas of computer science, including error-correcting codes [ref] , proof complexity [ref] , networks and distributed algorithms [ref] , and compressed sensing [ref] , among others.

New Explicit Constant-Degree Lossless Expanders · Introduction · 0.98

What it cites · 5 sentences without a confident label

Compares with 2 papers

Here, we compare our construction with two recent papers on similar topics [ref] [ref] .

Asymptotically Good Quantum and Locally Testable Classical LDPC Codes · Discussion · 1.00
Here, we compare our construction with two recent papers on similar topics [ref] [ref] .

Locally Testable Codes with constant rate, distance, and locality · Discussion · 1.00

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