Linear Complexity of Nonbinary Gordon–Mills–Welch Sequences
V.G. Starodubtsev · Journal of Communications Technology and Electronics · 2021
Abstract An expression for determining equivalent linear complexity (ELC) lS of p-ary (p > 2) Gordon–Mills–Welch sequences (GMWSs) with period N = pS – 1, formed in finite fields GF(pS) = GF[(pm)n] for n = 2 is presented. The expression was obtained based on the analysis of the ELC of known ternary sequences with periods N = 80 and 728 and pentary GMWSs with periods N = 24, 124, and 624, as well as taking into account the specificities of calculating the ELC for binary sequences. The ELC values are determined for ternary, pentary, septenary, undecimal, and tridecimal GMWSs the algorithms for which are missing in the known literature.