Subspace evasive sets

Zeev Dvir, Shachar Lovett
2012 Proceedings of the 44th symposium on Theory of Computing - STOC '12  
In this work we describe an explicit, simple, construction of large subsets of F n , 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 Pudlák and Rödl [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
more » ... nomial 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.
doi:10.1145/2213977.2214010 dblp:conf/stoc/DvirL12 fatcat:szj75lbozzfxpjfhrk6yhjoise