Determination of optimal period of absolute encoders with single track cyclic gray code

Low cost and miniaturized rotary encoders are important in automatic and precise production. Presented here is a code called Single Track Cyclic Gray Code (STCGC) that is an image etched on a single circular track of a rotary encoder disk read by a group of even spread reading heads to provide a unique codeword for every angular position and features such that every two adjacent words differ in exactly one component, thus avoiding coarse error. The existing construction or combination methods are helpful but not sufficient in determining the period of the STCGC of large word length and the theoretical approach needs further development to extend the word length. Three principles, such as the seed combination, short code removal and ergodicity examination were put forward that suffice determination of the optimal period for such absolute rotary encoders using STCGC with even spread heads. The optimal periods of STCGC in 3 through 29 bit length were determined and listed.