Abstract
A method for synthesis of Gordon–Mills–Welch sequences (GMWSs) over extended field GF[(2m)n], based on the relationship of the roots of check polynomial hМS(x) for the basic M-sequence (MS) with the roots of polynomial factors hсi(x) of check polynomial hGMWS(x) for a GMWS is considered. It is shown that the synthesis includes 1) an algorithm for determining polynomials hсi(x), based upon the use of p-conjugate elements with odd powers βr of an element belonging to subfield GF(2m), 2) an algorithm for determining the initial states of the shift registers constructed from polynomials hсi(x), which is based on the decimation of the symbols of the basis MS, 3) and a method for determining the complete lists of check polynomials hGMWS(x) for all primitive polynomials of field GF[(2m)n], based on which the basis MSs are formed.
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