Rate Amplification and Query-Efficient Distance Amplification for Linear LCC and LDC

Abstract

The main contribution of this work is a rate amplification procedure for LCC. Our procedure converts any q-query linear LCC, having rate ? and, say, constant distance to an asymptotically good LCC with q^poly(1/?) queries. Our second contribution is a distance amplification procedure for LDC that converts any linear LDC with distance ? 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/? asymptotically good LDC. This improves upon the poly(1/?) overhead obtained by the AEL distance amplification procedure [Alon and Luby, 1996; Alon et al., 1995]. 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