The algorithm for the formation of non-binary cascaded Gordon–Mills–Welch sequences

Based on a modification of the algorithm for determining the vector of decimation indices for the synthesis of binary cascaded Gordon–Mills–Welch sequences (CGMWS), an algorithm for the formation of non-binary CGMWS in the field GF[((pl)m)n] with a period N = pS–1 = plmn–1 has been developed, including a procedure for determining the vector of decimation indices А(l,m,n,r1,r2) = (d1,d2,…,dK) of the basic M-sequence (MS) and the procedure for calculating the vector of initial shifts С(l,m,n,r1,r2) of the summed sequences. The algorithm provides for the calculation of additional parametersvj, which are analogues of the parameter rin the expression to determine the resulting vector of decimation indices. The results of calculating the equivalent linear complexity (ELC) values of ternary cascaded and conventional GMWS for the period N = 38– 1 = 6560 are presented. It is shown that the ELC of cascaded sequences exceeds the ELC of conventional GMWSup to 10 times, with an increase in the period, the gain increases due to an increase in the number of combined vectors of decimation indices Аj(lmn, lm, vj).

finite fields, correlation function, M-sequences, non-binary cascaded Gordon–Mills–Welch sequences, equivalent linear complexity