  Reed Muller (RM) codes are known for their good minimum distance. One can use
their structure to construct polar-like codes with good distance properties by
choosing the information set as the rows of the polarization matrix with the
highest Hamming weight, instead of the most reliable synthetic channels.
However, the information length options of RM codes are quite limited due to
their specific structure. In this work, we present sufficient conditions to
increase the information length by at least one bit for some underlying RM
codes and in order to obtain pre-transformed polar-like codes with the same
minimum distance than lower rate codes.The proofs give a constructive method to
choose the row triples to be merged together to increase the information length
of the code and they follow from partitioning the row indices of the polar
encoding matrix with respect to the recursive structure imposed by the binary
representation of row indices. Moreover, our findings are combined with the
method presented in [2] to further reduce the number of minimum weight
codewords. Numerical results show that the designed codes perform close to the
meta-converse bound at short blocklengths and better than the
polarization-adjusted-convolutional polar codes with the same parameters.
