Dual Basis Based Processing of Wideband Gordon–Mills–Welch Sequences Based on Two Linear Registers

The paper presents a dual basis based algorithm for processing and determining the initial states of the shift registers that form the Gordon-Mills-Welch (GMW) wideband sequences, which are characterized by their greater number and higher structural secrecy than the widely used M sequences. It is shown that the proposed algorithm, in contrast to the known ones, allows one to determine arbitrary initial states of shift registers, which expands the possibilities of using composite wideband GMW sequences for solving various problems when transmitting information via communication channels with noise.