@inproceedings{a1b06a41bf9c4e40a0635ac1a52935bd,
title = "High Dimensional Expansion Implies Amplified Local Testability",
abstract = "In this work, we define a notion of local testability of codes that is strictly stronger than the basic one (studied e.g., by recent works on high rate LTCs), and we term it amplified local testability. Amplified local testability is a notion close to the result of optimal testing for Reed-Muller codes achieved by Bhattacharyya et al. We present a scheme to get amplified locally testable codes from high dimensional expanders. We show that single orbit Affine invariant codes, and in particular Reed-Muller codes, can be described via our scheme, and hence are amplified locally testable. This gives the strongest currently known testability result of single orbit affine invariant codes, strengthening the celebrated result of Kaufman and Sudan.",
keywords = "Amplified testing, High dimensional expanders, Locally testable codes",
author = "Tali Kaufman and Izhar Oppenheim",
note = "Publisher Copyright: {\textcopyright} Tali Kaufman and Izhar Oppenheim.; 25th International Conference on Approximation Algorithms for Combinatorial Optimization Problems and the 26th International Conference on Randomization and Computation, APPROX/RANDOM 2022 ; Conference date: 19-09-2022 Through 21-09-2022",
year = "2022",
month = sep,
day = "1",
doi = "10.4230/LIPIcs.APPROX/RANDOM.2022.5",
language = "الإنجليزيّة",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Amit Chakrabarti and Chaitanya Swamy",
booktitle = "Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2022",
address = "ألمانيا",
}
