Single-track circuit codes

Single-track circuit codes (STTCs) 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 first track. These codes simultaneously generalize single-track Gray codes and ordinary circuit codes. They are useful in angular quantization 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 STCCs for small lengths n⩽17 and spreads k⩽6, constructing some optimal and many good examples. We then give a general construction method for STCCs 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 STCCs for general spreads