  This paper proposes new polar code design principles for the low-latency
automorphism ensemble (AE) decoding. Our proposal permits to design a polar
code with the desired automorphism group (if possible) while assuring the
decreasing monomial property. Moreover, we prove that some automorphisms are
redundant under AE decoding, and we propose a new automorphisms classification
based on equivalence classes. Finally, we propose an automorphism selection
heuristic based on drawing only one element of each class; we show that this
method enhances the block error rate (BLER) performance of short polar codes
even with a limited number of automorphisms.
