Entropy Analysis of Galois LFSR-Based Pseudorandom Binary Sequence Generators

The problem of searching for aperiodic binary sequences with high entropy and uniform element distribution presents significant computational complexity, particularly as the sequence length increases. Such sequences are of crucial importance in communication engineering, radar systems[4], spectroscopy, quantum physics, chemistry, digital signal processing, and cryptography [3]. This paper examines the possibility of employing generators based on Galois fields, in particular linear feedback shift registers in Galois configuration (Galois LFSR), for constructing binary pseudorandom sequences and evaluating their entropic characteristics. A brief overview of the algebraic foundations of sequence generation in finite fields GF(2) through primitive polynomials is provided [2]. The obtained results can be applied to the design of signals with defined statistical properties, including high information density, which is critically important for spread spectrum systems and cryptographic protocols.