This paper provides an overview of trellis descriptions for block codes. Th
e design and implementation of efficient trellis decoders for the (32, 26)
and the (32, 21) BCH codes is then considered in some detail. Minimum edge
and vertex counts for the (32, 26) code are derived, and then generalized f
or arbitrary extended Hamming codes. A subcode analysis technique is used t
o tighten the lower bound on edge complexity for the (32, 21) code. A trell
is is then found that satisfies the optimized lower bound with equality.