Abstract. Two sets of sequences similar to Gordon-Mills-Welch (GMW) sequences in finite fields GF(2S) for values S=2 mod 4 are presented. Sets of GMW-like sequences are characterized by a five-level periodic autocorrelation and a four-level cross-correlation function. For these sets, the maximum value of the modulus of the mutual correlation function Rmax = (2S/2+1–1) is less than the same value for Gold sequences equal to (2S/2+1+1). The power of one of the sets, FFG1, is equal to half of the sequence period M1 = (N+1)/2 = 2S/2. All sequences of this set are balanced, that is, their weight is equal to V = 2S/2. The power of the other set of GMW- like sequences, FFG2, is approximately equal to the period of the sequences M2 = (N+1) = 2S/2. The sequences of FFG2 set are unbalanced, that is, their weight can take four values V = [2S/2-1(2S/2+1); 2S-1; 2S/2-1(2S/2–1); 2S/2 (2S/2-1–1)]. It is shown that formation of sets of GMW-like sequences with these power and correlation characteristics is possible only for periods N = 63, 1023, 16383, 262143, for which there exist GMW sequences with verification polynomials of degree 2S.

Keywords: finite fields, primitive polynomials, M-sequences, GMW-sequences, correlation function, structural secrecy

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