A fast algorithm to generate Beckett-Gray codes: Extended Abstract

We provide several heuristics to improve the efficiency of exhaustively generating Gray codes on length n binary strings. We then apply the heuristics to a restricted class of Gray codes on binary strings known as Beckett-Gray codes. The resulting algoirthm has a speed-up by a factor of 60 over the fastest previously known algorithm when n=6. It was also used to discover over 9500 new Beckett-Gray codes for n=7 in the equivalent of three months of computation time.