An algorithm to design prescribed length codes for single-tracked shaft encoders

Maximal-length binary shift register sequences have been known for a long time. They have many interesting properties, one of them is that when taken in blocks of n consecutive positions they form 2ⁿ - 1 different codes in a closed circular sequence. This property can be used for measuring absolute angular positions as the circle can be divided in as many parts as different codes can be retrieved. This paper describes how a closed binary sequence with arbitrary length can be effectively designed with the minimal possible block-length, using linear feedback shift registers (LFSR). Such sequences can be used for measuring a specified exact number of angular positions, using the minimal possible number of detectors allowed by linear methods.