After application of the channel transform, the synthetic channels follow a partial order with respect to their reliability [9]. This order is independent of channel that is used and therefore can be used for designing universally applicable polar codes. If a code is designed such that it complies with the partial order, it is called a decreasing monomial code.

An important property of decreasing monomial codes is their rich set of automorphisms. Automorphisms are permutations of the codeword bits that map the code onto itself, i.e., the permutation of any codeword is again a valid codeword. The automorphism group of decreasing monomial codes is the block lower triangular affine group (BLTA) [10].