  The Super-SAT or SSAT problem was introduced by Dinur et al.(2002,2003) to
prove the NP-hardness of approximation of two popular lattice problems -
Shortest Vector Problem(SVP) and Closest Vector Problem(CVP). They conjectured
that SSAT is NP-hard to approximate to within a factor of $n^c$ ($c>0$ is
constant), where $n$ is the size of the SSAT instance. In this paper we prove
this conjecture assuming the Projection Games Conjecture(PGC), given by
Moshkovitz (2012). This implies hardness of approximation of SVP and CVP within
polynomial factors, assuming PGC. We also reduce SSAT to the Nearest Codeword
Problem(NCP) and Learning Halfspace Problem(LHP), as considered by Arora et
al.(1997). This proves that both these problems are NP-hard to approximate
within a factor of $N^{c'/\log\log n}$($c'>0$ is constant) where $N$ is the
size of the instances of the respective problems. Assuming PGC these problems
are proved to be NP-hard to approximate within polynomial factors.
