  In this paper, code decompositions (a.k.a. code nestings) are used to design
binary polarization kernels. The proposed kernels are in general non-linear.
They provide a better polarization exponent than the previously known kernels
of the same dimensions. In particular, non-linear kernels of dimensions 14, 15,
and 16 are constructed and are shown to have optimal asymptotic
error-correction performance. The optimality is proved by showing that the
exponents of these kernels achieve a new upper bound that is developed in this
paper.
