SOME NEW CIRCUIT CODES

We present a new construction for snake-in-the-box codes and circuit c odes. Our technique is based on arranging necklaces, i.e. equivalence classes of words under cyclic shifting, to form codes and gives 21 new codes of lengths 8-17, all having more words than the best previously known codes. Included among these are two snake-in-the box codes: one of length 8 with 96 words, the other of length 10 with 340 words. We also report 15 new codes with small parameters. We prove the optimalit y of two of these codes and an already-known code. These last results were obtained using straightforward computer search.