Subspace evasive sets

In this work we describe an explicit, simple, construction of large subsets of Fn , where F is a finite field, that have small intersection with every k-dimensional affine subspace. Interest in the explicit construction of such sets, termed subspace-evasive sets, started in the work of Pudl´ak and R¨odl [PR04] who showed how such constructions over the binary field can be used to construct explicit Ramsey graphs. More recently, Guruswami [Gur11] showed that, over large finite fields (of size polynomial in n), subspace evasive sets can be used to obtain explicit listdecodable codes with optimal rate and constant list-size. In this work we construct subspace evasive sets over large fields and use them, as described in [Gur11], to reduce the list size of folded Reed-Solomon codes form poly(n) to a constant.

• Type: Journal
• Year: 2012
• Where: STOC
• Authors: Zeev Dvir, Shachar Lovett
• Keywords: Algorithms, Explicit Construction, Ramsey Graphs, Reed Solomon, STOC 2012