  The Learning with Errors problem (LWE) is one of the main candidates for
post-quantum cryptography. At Asiacrypt 2017, coded-BKW with sieving, an
algorithm combining the Blum-Kalai-Wasserman algorithm (BKW) with lattice
sieving techniques, was proposed. In this paper, we improve that algorithm by
using different reduction factors in different steps of the sieving part of the
algorithm. In the Regev setting, where $q = n^2$ and $\sigma =
n^{1.5}/(\sqrt{2\pi}\log_2^2 n)$, the asymptotic complexity is $2^{0.8917n}$,
improving the previously best complexity of $2^{{0.8927n}}$. When a quantum
computer is assumed or the number of samples is limited, we get a similar level
of improvement.
