  Recently, the authors showed that Reed-Muller (RM) codes achieve capacity on
binary memoryless symmetric (BMS) channels with respect to bit error rate. This
paper extends that work by showing that RM codes defined on non-binary fields,
known as generalized RM codes, achieve capacity on sufficiently symmetric
non-binary channels with respect to symbol error rate. The new proof also
simplifies the previous approach (for BMS channels) in a variety of ways that
may be of independent interest.
