Table 6 lists the properties of some distance-8
lexicodes and trellis-oriented
-codes. Over a binary field, lexicodes
with odd minimum distance are simply punctured lexicodes with even minimum distance, so it is redundant to list their
The minimum distance 4 lexicodes are all extended Hamming codes
or shortenings thereof .
The minimum distance 6 and 8 codes we have computed also have optimal
error-correction capability in
the sense that each has the best known minimum distance
for its length and dimension as compared to .
We can see that the trellis-oriented codes almost always have
lower decoding complexity than the corresponding lexicodes; however,
there are small pockets, where the trellis-oriented codes have
higher state complexity and/or decoding complexity than lexicodes.