  In this paper, we propose a new polar code construction by employing kernels
of different sizes in the Kronecker product of the transformation matrix, thus
generalizing the original construction by Arikan. The proposed multi-kernel
polar code allows for more flexibility in terms of the code length, moreover
allowing for various new design principles. We describe in detail encoding as
well as successive cancellation (SC) decoding and SC list (SCL) decoding, and
we provide a novel design method for the frozen set that allows to optimise the
performance under list decoding, as opposed to original relability-based code
design. Finally, we numerically demonstrate the advantage of multi-kernel polar
codes under the new design principles compared to punctured and shortened polar
codes.
