  We consider the problem of distilling uniform random bits from an unknown
source with a given $p$-entropy using linear hashing. As our main result, we
estimate the expected $p$-divergence from the uniform distribution over the
ensemble of random linear codes for all integer $p\ge 2$. The proof relies on
analyzing how additive noise, determined by a random element of the code from
the ensemble, acts on the source distribution. This action leads to the
transformation of the source distribution into an approximately uniform one, a
process commonly referred to as distribution smoothing. We also show that
hashing with Reed-Muller matrices reaches intrinsic randomness of memoryless
Bernoulli sources in the $l_p$ sense for all integer $p\ge 2$.
