WebThe natural probabilistic test for membership in a product code C is the following. Deflnition 7 (Product Tester). Given a product code C = C1 ›C2, test a matrix r for membership in C as follows: °ip a coin; if it is heads, test whether a random row of r is a codeword of C1; if it is tails, test whether a random column of r is a codeword of C2. It is straightforward to show … WebGoldreich, O., Sudan, M.: Locally testable codes and PCPs of almost-linear length. In: Proc. 43rd IEEE Symp. on Foundations of Computer Science, pp. 13–22 (2002) Google Scholar Valiant, P.: The tensor product of two codes is not necessarily robustly testable. In: APPROX-RANDOM, pp. 472–481 (2005) Google Scholar
Two-sided Robustly Testable Codes
WebTwo-sided Robustly Testable Codes. CoRR abs/2206.09973 (2024) 2024 [j1] view. electronic edition via DOI (open access) references & citations; authority control ... Asymptotically Good Quantum and Locally Testable Classical LDPC Codes. CoRR abs/2111.03654 (2024) 2024 [i3] view. electronic edition @ arxiv.org (open access) references & citations ... 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, which ensured their linear minimum distance. We hope that the existence of such codes with a stronger form of robustness, ... can i lay on my stomach at 5 months pregnant
Two-sided Robustly Testable Codes - NASA/ADS
WebAug 22, 2005 · 2004. TLDR. The notion of robust local testability of codes is introduced, and codes built by tensor products can be tested robustly and somewhat locally by applying a … 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 … WebWe show that expander codes and locally-testable codes are smooth. This complements recent examples of P. Valiant [13] and Coppersmith and Rudra [9] of codes whose tensor product is not robustly testable. 1 Introduction A binary linear code is a linear subspace C ⊆{0,1}n.Acodeislocally testable can i lay on my stomach for an mri