Dinur-Lin-Vidick (DLV) code[1]
Description
Member of a family of quantum locally testable codes constructed using cubical chain complexes, which are \(t\)-order extensions of the complexes underlying expander codes (\(t=1\)) and expander lifted-product codes (\(t=2\)).
For \(t=4\), assuming a conjecture about random linear maps, there exists a family with linear dimension and inverse poly-logarithmic relative distance and soundness. Applying weight reduction yields \(\Omega(1/\text{polylog}n)\) soundness, distance, and dimension, but \(\Theta(n)\) locality [2; Table 4]. Applying distance amplification and soundness amplification yields asymptotically constant soundness, \(\Theta(n)\) distance, \(\Theta(n)\) dimension, but poly-logarithmic locality [2; Table 4].
Parent
Cousin
- Quantum locally testable code (QLTC) — DLV codes have linear dimension and inverse poly-logarithmic relative distance and soundness, assuming a conjecture about random linear maps [1]. Applying distance amplification and soundness amplification yields asymptotically constant soundness, \(\Theta(n)\) distance, \(\Theta(n)\) dimension, but poly-logarithmic locality [2; Table 4].
References
- [1]
- I. Dinur, T.-C. Lin, and T. Vidick, “Expansion of higher-dimensional cubical complexes with application to quantum locally testable codes”, (2024) arXiv:2402.07476
- [2]
- A. Wills, T.-C. Lin, and M.-H. Hsieh, “Tradeoff Constructions for Quantum Locally Testable Codes”, (2024) arXiv:2309.05541
Page edit log
- Victor V. Albert (2024-02-13) — most recent
Cite as:
“Dinur-Lin-Vidick (DLV) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/dlv