DOI 10.17586/0021-3454-2024-67-2-107-115
UDC 519.725
FORMATION OF SETS OF FIVE-FOLD GOLD-TYPE SEQUENCES FOR DIGITAL INFORMATION TRANSMISSION SYSTEMS
Multiservice Nets and Telecommunications, Ltd., St. Petersburg; Head of Department
V. V. Tkachenko
A. F. Mozhaisky Military Space Academy;
Reference for citation: Starodubtsev V. G., Tkachenko V. V. Formation of sets of five-fold Gold-type sequences for digital information transmission systems. Journal of Instrument Engineering. 2024. Vol. 67, N 2. P. 107—115 (in Russian). DOI: 10.17586/0021-3454-2024-67-2-107-115.
Abstract. Sets of vectors of decimation indices IS = (id1, id2, …, idn) for the formation of sets of five-fold Gold-type sequences in finite fields GF(5S) (S = 3, 4, 5, 6) based on М- sequences with verification polynomials hМП(x) for periods N = 5S – 1 < 20 000, are presented. The sets include both the well–known decimation indices obtained by Trachtenberg, Helleset, Kumar and satisfying the condition LCD(idi, 5S – 1) = 1 (LCD is the largest common divisor), and the newly found indices that allow the formation of sets of five-fold Gold-type sequences with volumes VS = N + 1 and low levels of periodic auto- and the cross-correlation functions. For the considered values of S, boundary estimates of the maximum value of the correlation function modulus Rmax are given.
Abstract. Sets of vectors of decimation indices IS = (id1, id2, …, idn) for the formation of sets of five-fold Gold-type sequences in finite fields GF(5S) (S = 3, 4, 5, 6) based on М- sequences with verification polynomials hМП(x) for periods N = 5S – 1 < 20 000, are presented. The sets include both the well–known decimation indices obtained by Trachtenberg, Helleset, Kumar and satisfying the condition LCD(idi, 5S – 1) = 1 (LCD is the largest common divisor), and the newly found indices that allow the formation of sets of five-fold Gold-type sequences with volumes VS = N + 1 and low levels of periodic auto- and the cross-correlation functions. For the considered values of S, boundary estimates of the maximum value of the correlation function modulus Rmax are given.
Keywords: finite fields, Gold sequences, correlation function, M-sequences, decimation indices
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