Formation of Septenary Gordon–Mills–Welch Sequences for Digital Information Transmission Systems
V.G. Starodubtsev · Journal of Communications Technology and Electronics · 2022
Abstract In this paper, we present septenary Gordon–Mills–Welch sequences (GMWSs) with a period of N = 2400 that are formed in finite GF[(7m)]n = GF(7S) fields. Checking polynomials hGMWS(x) are obtained in the form of a product of both primitive and irreducible polynomials hсi(x) with a degree of S = 4. The formation of GMWSs by summing sequences with polynomials hсi(x) is shown to require knowledge of the symbols of the M-sequence (MS) with polynomial hMS(x) and decimation indices determined by the exponents of the roots of polynomials hсi(x). It is determined that, compared to the binary case, septenary summable sequences can have an initial shift that is a multiple of N/(p – 1) = 400. It is shown that for each of the 160 primitive polynomials of degree S = 4 in the GF(74) field, it is possible to form seven GMWSs with equivalent linear complexity ls from 12 to 84. Compared to septenary MSs, the maximal gain in structural secrecy is 21 times.