Methods and systems for determining characteristics of a sequence of n-state symbols

摘要

Maximum length properties of n-state sequences of n-state symbols with n=2 or n>2 are tested. Checkwords are generated from p consecutive n-state symbols in a sequence of n-state symbols which may overlap by (p−1) n-state symbols. If a sequence has np−1 n-state symbols in which 2 consecutive checkwords overlap in (p−1) n-state symbols and each checkword formed in the extended sequence is unique, then the sequence is a maximum length n-state sequence. An n-state feedback shift register based sequence generator with p n-state register elements is tested on the content of the shift register for np−1 cycles. If the shift register content is not repeated the sequence is maximum length. Generation of a sequence is stopped when the content repeats. Non-reversible n-state inverters and non-reversible n-state logic functions are applied to generate n-state sequences.

主权项

1. A method for testing a property of a sequence of at least k n-state symbols with n an integer greater than 1 and k an integer greater than 2, each n-state symbol being represented by a signal, comprising:
a processor selecting a first n-state inverter from a plurality of n-state inverters and implementing the first n-state inverter in a shift register of p n-state shift register elements with feedback with p an integer greater than 1 and at least one n-state switching function; the processor generating n-state symbols in the sequence by a sequence generator that is defined by a first configuration that includes the n-state feedback shift register of p n-state shift register elements, the first n-state inverter and the at least one n-state switching function, wherein each generated n-state symbol corresponds with a content of the shift register of p n-state symbols, wherein the processor generates a first n-valued symbol and stores a corresponding first content of the shift register of p n-state symbols in a memory; the processor generating a kth n-valued symbol in the sequence of at least k n-state symbols based on a kth content of the shift register; and the processor comparing the kth shift register content of p n-state symbols with the first content of the shift register of p n-state symbols corresponding with generating the first n-state symbol in the sequence of n-state symbols to determine if the first content of the shift register of p n-valued symbols is repeated to decide to generate the next symbol in the sequence of n-state symbols.