Single-track circuit codes

Single-track circuit codes (STTCs) are circuit codes with codewords of leng th n such that all the n tracks which correspond to the n distinct coordina tes of the codewords are cyclic shifts of the first track. These codes simu ltaneously generalize single-track Gray codes and ordinary circuit codes. T hey are useful in angular quantization applications in which error detectin g and/or correcting capabilities are needed. A parameter k, called the spre ad of the code, measures the strength of this error control capability. We consider the existence of STCCs for small lengths n less than or equal to 1 7 and spreads k less than or equal to 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 import ance. We also use the construction to prove a general result on the existen ce of STCCs for general spreads.