TY - GEN
T1 - High Dimensional Expansion Implies Amplified Local Testability
AU - Kaufman, Tali
AU - Oppenheim, Izhar
N1 - Funding Information:
Funding Tali Kaufman: This work was partially funded by ERC grant no. 336283 and BSF grant no. 2012256. Izhar Oppenheim: This work was partially funded by ISF grant no. 293/18.
Publisher Copyright:
© Tali Kaufman and Izhar Oppenheim.
PY - 2022/9/1
Y1 - 2022/9/1
N2 - 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.
AB - 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.
KW - Amplified testing
KW - High dimensional expanders
KW - Locally testable codes
UR - http://www.scopus.com/inward/record.url?scp=85139132672&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.APPROX/RANDOM.2022.5
DO - 10.4230/LIPIcs.APPROX/RANDOM.2022.5
M3 - Conference contribution
AN - SCOPUS:85139132672
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2022
A2 - Chakrabarti, Amit
A2 - Swamy, Chaitanya
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 25th International Conference on Approximation Algorithms for Combinatorial Optimization Problems and the 26th International Conference on Randomization and Computation, APPROX/RANDOM 2022
Y2 - 19 September 2022 through 21 September 2022
ER -
