Single-track Gray codes are a special class of Gray codes which have advantages over conventional Gray codes in certain quantization and coding applications. The problem of constructing high period single-track Gray codes is considered. Three iterative constructions are given, along with a heuristic method for obtaining good seed-codes. In combination, these yield many families of very high period single-track Gray codes. In particular, for m > 3 , length 'r~ = 2", period 2" -2n codes are obtained.
Index Terms-Graycodes, heuristic methods, inequivalent sequences, necklaces, quantization, recursive construction, self-dual sequences 2n 5 P 5 2". Examples of high period codes for small n were given in [9], along with a general construction for single-track Gray resulting in a small angular error.codes which leads to the following: