  The binary primitive BCH codes are cyclic and are constructed by choosing a
subset of the cyclotomic cosets. Which subset is chosen determines the
dimension, the minimum distance and the weight distribution of the BCH code. We
construct possible BCH codes and determine their coderate, true minimum
distance and the non-equivalent codes. A particular choice of cyclotomic cosets
gives BCH codes which are, extended by one bit, equivalent to Reed-Muller
codes, which is a known result from the sixties. We show that BCH codes have
possibly better parameters than Reed-Muller codes, which are related in recent
publications to polar codes. We study the decoding performance of these
different BCH codes using information set decoding based on minimal weight
codewords of the dual code. We show that information set decoding is possible
even in case of a channel without reliability information since the decoding
algorithm inherently calculates reliability information. Different BCH codes of
the same rate are compared and different decoding performances and complexity
are observed. Some examples of hard decision decoding of BCH codes have the
same decoding performance as maximum likelihood decoding. All presented
decoding methods can possibly be extended to include reliability information of
a Gaussian channel for soft decision decoding. We show simulation results for
soft decision list information set decoding and compare the performance to
other methods.
