We show that the closest vector problem with preprocessing (CVPP) is NP-hard to approximate to within /spl radic/3-/spl epsi/ for any /spl epsi/>0. In addition, we show that the nearest codeword problem with preprocessing (NCPP) is NP-hard to approximate to within 3-/spl epsi/. These results improve the results of Feige and Micciancio (2002). We also present the first inapproximability result for the relatively nearest codeword problem with preprocessing (RNCP). Finally, we describe an n-approximation algorithm to CVPP.
['Oded Regev']
Improved inapproximability of lattice and coding problems with preprocessing