FORMATION SEQUENCES OF GORDON — MILLS — WELCH WITH PERIOD N = 511
Annotation
Based on developed algorithm for generating Gordon — Mills — Welch sequences, a full list of testing polynomials for GMW-sequences with the period N = 511 is obtained. Binary GMW-sequences are formed on the basis of base M-sequence over finite fields with double expansion GF[(2m)n] and can be represented as a matrix of dimension [JxL]=[(2m–1)x(2m+1)]. A qualitative specifics of sequences with the period N = 511 consists in the fact that they are formed over a finite field GF[(23)3] and are presented in the form of a matrix of dimension [JxL]=[7x73], but not in the form of quasi-quadratic matrix of dimension [(2m–1)x(2m+1)]. Equivalent linear complexity of these sequences corresponds to the degree of the testing polynomial which can be represented as a product of three irreducible polynomials of the ninth degree. GMW-sequences with period N = 511 are formed using M-sequences of the same period. There are 48 primitive polynomials of the ninth degree in the field GF(29), the full list also contains 48 test polynomials for GMW-sequences.
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