Single-track circuit codes

Single-track circuit codes are circuit codes with codewords of length n such that all the n tracks which correspond to the n distinct coordinates of the codewords are cyclic shifts of the rst track. These codes simul taneously generalise single-track Gray codes and ordinary circuit codes. They are useful in angular quantisation applications in which error detecting and/or correcting capabilities are needed. A parameter, k, called the spread of the code, measures the strength of this error control capability. We consider the existence of single-track circuit codes for small lengths n 17 and spreads k 6, constructing some optimal and many good examples. We then give a general construction method for single-track circuit codes which makes use of ordinary circuit codes. We use this construction to construct examples of codes with 360 and 1000 codewords which are of practical importance. We also use the construction to prove a general result on the existence of single-track circuit codes for general spreads.