Two-sided robustly testable codes

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August undefined, 2024

WebPavel Panteleev's 9 research works with 157 citations and 186 reads, including: Two-sided Robustly Testable Codes WebWe show that the tensor product of two random linear codes is robustly testable with high probability. This implies that one can obtain pairs of linear codes such that their product and the product of their dual codes are simultaneously robustly testable. Such two-sided robustly testable codes (with a much weaker form of robustness) were the key ingredient …

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WebBen-Sasson and Sudan [6] showed that a code obtained by tensoring three or more codes (i.e. a code of the form C 1 ⊗C 2 ⊗C 3) is robustly testable, and used this result to construct LTCs. For the tensor product of two codes R and C, they considered the following natural test, and asked whether it is robust: WebThis implies that one can obtain pairs of linear codes such that their product and the product of their dual codes are simultaneously robustly testable. Such two-sided robustly testable codes (with a much weaker form of robustness) were the key ingredient in the recent constructions of asymptotically good quantum LDPC codes, which ensured their linear … hinckley motorcycle training scheme

Two-sided Robustly Testable Codes - Semantic Scholar

WebNov 30, 2024 · Two-sided Robustly Testable Codes. June 2024. Gleb Kalachev; Pavel Panteleev; We show that the tensor product of two random linear codes is robustly testable with high probability. WebA class of codes is described having checkMatrices which are the tensor product of the check matrices of known nonbinary codes and binary codes which correct random bursts of errors and bursts of burst of errors. A class of codes is described having check matrices which are the tensor product of the check matrices of known nonbinary codes and binary … WebTwo-sided Robustly Testable Codes. Preprint. Jun 2024; Gleb Kalachev; Pavel Panteleev; We show that the tensor product of two random linear codes is robustly testable with high … homelessness day 2023

Two-sided Robustly Testable Codes - NASA/ADS

Robust local testability of tensor products of LDPC codes

WebC is said to be robustly testable if it has a (1)-robust tester. Given two codes C1 and C2 with parameters k1;n1;d1 and k2;n2;d2 their tensor product, denoted by C1 C2, consists of n2 n1 matrices such that every row of the matrix is a codeword in C1 and every column is a codeword in C2. It is well known that C3 = C1 C2 has the parameters WebNov 2, 2024 · 11/02/22 - We present new constructions of binary quantum codes from quaternary linear Hermitian self-dual codes. ... Two-sided Robustly Testable Codes We show that the tensor product of two random linear codes is robustly t ... hinckley motor sportsWebNov 8, 2024 · Two-sided Robustly Testable Codes. G. Kalachev, Pavel Panteleev; Computer Science. ArXiv. 2024; We show that the tensor product of two random linear codes is … hinckley motorcycle shop

"WebFeb 16, 2006 · Next, we show that codes built by tensor products can be tested robustly and somewhat locally by applying a variant of a test and proof technique introduced by Raz and Safra in the context of testing low‐degree multivariate polynomials (which are a special case of tensor codes). Combining these two results gives us a generic construction of ... " - Two-sided robustly testable codes

Two-sided robustly testable codes

WebApr 30, 2012 · Two-sided Robustly Testable Codes. 2024, arXiv. Locally Testable Codes with constant rate, distance, and locality. 2024, arXiv. On List Recovery of High-Rate Tensor Codes. 2024, IEEE Transactions on Information Theory. Local proofs approaching the witness length [extended abstract] WebBen-Sasson and Sudan show that the repeated tensor product of codes leads to a general class of locally testable codes. ... Valiant, P. (2005). The Tensor Product of Two Codes Is Not Necessarily Robustly Testable. In: Chekuri, C., Jansen, K., Rolim, J.D.P., Trevisan, L. (eds) Approximation, Randomization and Combinatorial Optimization.

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WebThis implies that one can obtain pairs of linear codes such that their product and the product of their dual codes are simultaneously robustly testable. Such two-sided robustly testable codes (with a much weaker form of robustness) were the key ingredient in the recent constructions of asymptotically good quantum LDPC codes, which ensured their linear … WebJun 20, 2024 · Two-sided Robustly Testable Codes. We show that the tensor product of two random linear codes is robustly testable with high probability. This implies that one can …

WebGleb Kalachev's 20 research works with 192 citations and 245 reads, including: Two-sided Robustly Testable Codes WebTwo-sided Robustly Testable Codes. We show that the tensor product of two random linear codes is robustly t... 0 Gleb Kalachev, et al. ∙. share. research. ∙ 12 months ago.

WebSuch two-sided robustly testable codes (with a much weaker form of robustness) were the key ingredient in the recent constructions of asymptotically good quantum LDPC codes, …

WebJun 20, 2024 · Such two-sided robustly testable codes (with a much weaker form of robustness) were the key ingredient in the recent constructions of asymptotically good …

WebJan 1, 1994 · Such two-sided robustly testable codes (with a much weaker form of robustness) were the key ingredient in the recent constructions of asymptotically good quantum LDPC codes, which ensured their ... hinckley motor spares hinckleyWebSep 27, 2024 · Two-sided Robustly Testable Codes. CoRR abs/2206.09973 (2024) 2024 [j1] view. electronic edition via DOI (open access) references & citations; authority ... Asymptotically Good Quantum and Locally Testable Classical LDPC Codes. CoRR abs/2111.03654 (2024) 2024 [i2] view. electronic edition @ arxiv.org (open access) … hinckley motor sparesWebSuch two-sided robustly testable codes (with a much weaker form of robustness) were the key ingredient in the recent constructions of asymptotically good quantum LDPC codes, which ensured their linear minimum distance. We hope that the existence of such codes with a stronger form of robustness, ... homelessness dashboard seattleWebUpload an image to customize your repository’s social media preview. Images should be at least 640×320px (1280×640px for best display). homelessness declarationWebApr 30, 2012 · Two-sided Robustly Testable Codes. 2024, arXiv. Locally Testable Codes with constant rate, distance, and locality. 2024, arXiv. On List Recovery of High-Rate … hinckley mumsnetWebThis implies that one can obtain pairs of linear codes such that their product and the product of their dual codes are simultaneously robustly testable. Such two-sided robustly … hinckley motorcycle trainingWebThis implies that one can obtain pairs of linear codes such that their product and the product of their dual codes are simultaneously robustly testable. Such two-sided robustly … homelessness definition government