The Projection Games Conjecture and the hardness of approximation of super-SAT and related problems

The Super-SAT (SSAT) problem was introduced in [1], [2] to prove the NP-hardness of approximation two popular lattice problems - Shortest Vector Problem and Closest Problem. SSAT is conjectured be NP-hard approximate within a factor nc (c positive constant, n size instance). In this paper we conjecture assuming Projection Games Conjecture (PGC) [3]. This implies hardness these polynomial factors, PGC. We also reduce Nearest Codeword Learning Halfspace [4]. proves that both are Nc?/log?log?n (c? N instances respective problems). Assuming PGC proved factors.