TY - GEN
T1 - Rate amplification and query-efficient distance amplification for linear LCC and LDC
AU - Cohen, Gil
AU - Yankovitz, Tal
N1 - Publisher Copyright:
© Gil Cohen and Tal Yankovitz; licensed under Creative Commons License CC-BY 4.0
PY - 2021/7/1
Y1 - 2021/7/1
N2 - The main contribution of this work is a rate amplification procedure for LCC. Our procedure converts any q-query linear LCC, having rate ρ and, say, constant distance to an asymptotically good LCC with qpoly(1/ρ) queries. Our second contribution is a distance amplification procedure for LDC that converts any linear LDC with distance δ and, say, constant rate to an asymptotically good LDC. The query complexity only suffers a multiplicative overhead that is roughly equal to the query complexity of a length 1/δ asymptotically good LDC. This improves upon the poly(1/δ) overhead obtained by the AEL distance amplification procedure [2, 1]. Our work establishes that the construction of asymptotically good LDC and LCC is reduced, with a minor overhead in query complexity, to the problem of constructing a vanishing rate linear LCC and a (rapidly) vanishing distance linear LDC, respectively.
AB - The main contribution of this work is a rate amplification procedure for LCC. Our procedure converts any q-query linear LCC, having rate ρ and, say, constant distance to an asymptotically good LCC with qpoly(1/ρ) queries. Our second contribution is a distance amplification procedure for LDC that converts any linear LDC with distance δ and, say, constant rate to an asymptotically good LDC. The query complexity only suffers a multiplicative overhead that is roughly equal to the query complexity of a length 1/δ asymptotically good LDC. This improves upon the poly(1/δ) overhead obtained by the AEL distance amplification procedure [2, 1]. Our work establishes that the construction of asymptotically good LDC and LCC is reduced, with a minor overhead in query complexity, to the problem of constructing a vanishing rate linear LCC and a (rapidly) vanishing distance linear LDC, respectively.
KW - Locally correctable codes
KW - Locally decodable codes
UR - http://www.scopus.com/inward/record.url?scp=85115323009&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.CCC.2021.1
DO - 10.4230/LIPIcs.CCC.2021.1
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AN - SCOPUS:85115323009
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 36th Computational Complexity Conference, CCC 2021
A2 - Kabanets, Valentine
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 36th Computational Complexity Conference, CCC 2021
Y2 - 20 July 2021 through 23 July 2021
ER -