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

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 q poly(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.