On the eigenvalue and Shannon's entropy of finite length random sequences

Abstract

Pseudorandom binary sequences play a significant role in many fields, such as spread spectrum communications, stochastic computation, and cryptography. The complexity measures of sequences and their relationship still remain an interesting open problem. In this article, we study on the eigenvalue of random sequences, deduce its theoretical expectation and variance of random sequences with length N, and establish the relationship between eigenvalue and Shannon's entropy. The results show that these two measures are consistent. Furthermore, the eigenvalue of random n‐block sequences and its relation to Shannon's entropy are also been studied. © 2014 Wiley Periodicals, Inc. Complexity 21: 154–161, 2015