CRT and Fixed Patterns in Combinatorial Sequences

Abstract: In this paper, new context of Chinese Remainder Theorem (CRT) based analysis of combinatorial sequence generators has been presented. CRT is exploited to establish fixed patterns in LFSR sequences and underlying cyclic structures of finite fields. New methodology of direct computations of DFT spectral points in higher finite fields from known DFT spectra points of smaller constituent fields is also introduced. Novel approach of CRT based structural analysis of LFSR based combinatorial sequence is given both in time and frequency domain. The proposed approach is demonstrated on some examples of combiner generators and is scalable to general configuration of combiner generators.