Some New Circuit Codes

Let n/spl ges/1 and suppose C=W/sub 0/,W/sub 1/,...,W/sub t-1/ is a list of t length n binary words. For 1/spl les/k/spl les/n we say that C is a length n, spread k circuit code if for every i,j with 0/spl les/i,j<t, d/sub H/(W/sub i/,W/sub i+1/)=1, d/sub H/(W/sub i/,W/sub j/)<k/spl rArr/d/sub c/(W/sub i/,W/sub j/)=d/sub H/(W/sub i/,W/sub j/) where subscripts are reduced modulo t, d/sub H/ denotes Hamming distance and d/sub c/ denotes the number of places between the two words in the list C. Codes of spread 2 are also known as snake-in-the-box codes. For given n and k, it is of interest to maximise the number of words in such a code, as this increases the resolution that can be achieved. We present a new construction for circuit codes, yielding many codes better than those previously known.