Great results! ]The fact that a code having this 4-fold symmetry, which singles out one
pair of bits (c and h above), beats the best codes with the much more uniform 5-fold rotational symmetry, gives me the impression that symmetry is useful more because it cuts down the search space than because large codes are likely to be highly symmetric.
--Michael
I sort of half-agree. With the Rubik's cube, positions with symmetry tend to have more extremal properties because there are fewer "distinct" paths to start (for instance); a similar thing may be happening here. So not only does symmetry cut down the search, but symmetrical positions also tend to have more interesting properties. -tom -- -- http://cube20.org/ -- http://golly.sf.net/ --