Some new circuit codes

Let n⩾1 and suppose C=W₀,W₁,…,W _t-1 is a list of t length n binary words. For 1⩽k⩽n we say that C is a length n, spread k circuit code if for every i,j with 0⩽i,j<t, d_H(W_i,W_i+1)=1, d_H (W_i,W_j)<k⇒d_c(W_i ,W_j)=d_H(W_i,W_j) where subscripts are reduced modulo t, d_H denotes Hamming distance and d_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