Algorithm for Generating Extra-Long Gordon-Mills-Welch Sequences

摘要

The modification of an algorithm for determining polynomial multipliers h(ci)(x) of test polynomial h(GMWS)(x), which is the main component of the method for synthesizing Gordon-Mills-Welch sequences (GMWSs), is set as a basis for developing the software implementation of the algorithm for generating extra-long GMWSs having a two-level periodic autocorrelation function and high structural latency and generated over the finite field with double extension GF(2(S)) = GF[(2(m))(n)]. In the modified algorithm, the expressions for the number of operations in computing the vector of alternatives, from which the vector of decimation indices is formed, are derived for different values of parameter n. These expressions also serve as upper estimates for the number of summed sequences. To generate extra-long GMWSs with periods from N = 2(12) - 1 = 4095 to N = 2(20) - 1 = 1 048 575, the sets of vectors of decimation indices are obtained for admissible values of parameters m and n.