ECCC-Report TR11-139https://eccc.weizmann.ac.il/report/2011/139Comments and Revisions published for TR11-139en-usWed, 26 Oct 2011 04:25:11 +0200
Paper TR11-139
| Subspace Evasive Sets |
Zeev Dvir,
Shachar Lovett
https://eccc.weizmann.ac.il/report/2011/139 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 Pudlak and Rodl (2004) who showed how such constructions over the binary field can be used to construct explicit Ramsey graphs. More recently, Guruswami (2011) showed that, over large finite fields (of size polynomial in n), subspace evasive sets can be used to obtain explicit list-decodable codes with optimal rate and constant list-size. In this work we construct subspace evasive sets over large fields and use them to reduce the list size of folded Reed-Solomon codes form poly(n) to a constant.Wed, 26 Oct 2011 04:25:11 +0200https://eccc.weizmann.ac.il/report/2011/139