Locally testable codes with constant rate, distance, and locality
A locally testable code (LTC) is an error correcting code that has a property-tester. The tester
reads q bits that are randomly chosen, and rejects words with probability proportional to their …
reads q bits that are randomly chosen, and rejects words with probability proportional to their …
Decodable Quantum LDPC Codes beyond the Distance Barrier Using High-Dimensional Expanders
Constructing quantum low-density parity-check (LDPC) codes with a minimum distance that
grows faster than a square root of the length has been a major challenge of the field. With …
grows faster than a square root of the length has been a major challenge of the field. With …
Expander graphs in pure and applied mathematics
A Lubotzky - Bulletin of the American Mathematical Society, 2012 - ams.org
Expander graphs are highly connected sparse finite graphs. They play an important role in
computer science as basic building blocks for network constructions, error correcting codes …
computer science as basic building blocks for network constructions, error correcting codes …
[PDF][PDF] Characterizing Direct Product Testing via Coboundary Expansion
M Bafna, D Minzer - Proceedings of the 56th Annual ACM Symposium on …, 2024 - dl.acm.org
A d-dimensional simplicial complex X is said to support a direct product tester if any locally
consistent function defined on its k-faces (where k≪ d) necessarily come from a function …
consistent function defined on its k-faces (where k≪ d) necessarily come from a function …
[HTML][HTML] Explicit constructions of Ramanujan complexes of type Ad
Explicit constructions of Ramanujan complexes of type Ãd - ScienceDirect Skip to main
contentSkip to article Elsevier logo Journals & Books Search RegisterSign in View PDF …
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Stability of homomorphisms, coverings and cocycles ii: Examples, applications and open problems
Coboundary expansion (with F 2 coefficients), and variations on it, have been the focus of
intensive research in the last two decades. It was used to study random complexes, property …
intensive research in the last two decades. It was used to study random complexes, property …
High dimensional expanders imply agreement expanders
I Dinur, T Kaufman - 2017 IEEE 58th Annual Symposium on …, 2017 - ieeexplore.ieee.org
We show that high dimensional expanders imply derandomized direct product tests, with a
number of subsets that is linear in the size of the universe. Direct product tests belong to a …
number of subsets that is linear in the size of the universe. Direct product tests belong to a …
Simplicial complexes: spectrum, homology and random walks
This paper studies the dynamical and asymptotic aspects of high‐dimensional expanders.
We define a stochastic process on simplicial complexes of arbitrary dimension, which …
We define a stochastic process on simplicial complexes of arbitrary dimension, which …
Approximating constraint satisfaction problems on high-dimensional expanders
We consider the problem of approximately solving constraint satisfaction problems with arity
k> 2 (kCSPs) on instances satisfying certain expansion properties, when viewed as …
k> 2 (kCSPs) on instances satisfying certain expansion properties, when viewed as …
Quasi-linear size pcps with small soundness from hdx
We construct 2-query, quasi-linear size probabilistically checkable proofs (PCPs) with
arbitrarily small constant soundness, improving upon Dinur's 2-query quasi-linear size PCPs …
arbitrarily small constant soundness, improving upon Dinur's 2-query quasi-linear size PCPs …