  In this paper we deal with polar code automorphisms that are beneficial under
low-latency automorphism ensemble (AE) decoding, and we propose polar code
designs that have such automorphisms. Successive-cancellation (SC) decoding and
thus SC-based AE decoding are invariant with respect to the only known polar
code automorphisms, namely those of the lower-triangular affine (LTA) group. To
overcome this problem, we provide methods to determine whether a given polar
code has non-LTA automorphisms and to identify such automorphisms. Building on
this, we design specific polar codes that admit automorphisms in the
upper-diagonal linear (UTL) group, and thus render SC-based AE decoding
effective. Demonstrated by examples, these new polar codes under AE decoding
outperform conventional polar codes under SC list decoding in terms of error
rate, while keeping the latency comparable to SC decoding.
