Sets of GMW-like sequences for digital information transmission and processing systems

Abstract

Two sets of sequences similar to Gordon-Mills-Welch (GMW) sequences in finite fields GF(2^S) 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 |R^max| = (2^S/2+1–1) is less than the same value for Gold sequences equal to (2^S/2+1+1). The power of one of the sets, FF_G1, is equal to half of the sequence period M₁ = (N+1)/2 = 2^S/2. All sequences of this set are balanced, that is, their weight is equal to V = 2^S/2. The power of the other set of GMW- like sequences, FF_G2, is approximately equal to the period of the sequences M₂ = (N+1) = 2_S/2. The sequences of FF_G2 set are unbalanced, that is, their weight can take four values V = [2^S/2-1(2^S/2+1); 2^S-1; 2^S/2-1(2^S/2–1); 2^S/2 (2^S/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 2^S.