DOI 10.17586/0021-3454-2023-66-7-568-575
UDC 519.725
FORMATION OF SETS OF TERNARY GOLD-LIKE SEQUENCES FOR DIGITAL INFORMATION TRANSMISSION AND PROCESSING SYSTEMS
Multiservice Nets and Telecommunications, Ltd., St. Petersburg; Head of Department
V. V. Myshko
A. F. Mozhaisky Military Space Academy, Department of Technologies and Means of Automation of Processing and Analysis of Space Facilities Information ; Senior Lecturer
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Reference for citation: Starodubtsev V. G., Myshko V. V. Formation of sets of ternary Gold-like sequences for digital information transmission and processing systems. Journal of Instrument Engineering. 2023. Vol. 66, N 7. P. 568—575 (in Russian). DOI: 10.17586/0021-3454-2023-66-7-568-575.
Abstract. Sets of vectors of decimation indices IS(id1, id2, ..., idn) of ternary M-sequences (MS) with verification polynomials hMP(x) for periods N = 3S–1 < 20000 formed in finite fields GF(3S) for S = 3, 5, 7, 9 are presented. The sets include both the well–known decimation indices and the newly obtained indices that allow formatting sets of ternary Gold-like sequences (GLS) with a volume of N+2 and a low level of values of the periodic cross-correlation function. For the value S = 5, four additional indices were obtained to five known decimation indices, for S = 7, ten decimation indices were added to seven known indices, and for S = 9, nine decimation indices were additionally obtained to nine known indices.
Abstract. Sets of vectors of decimation indices IS(id1, id2, ..., idn) of ternary M-sequences (MS) with verification polynomials hMP(x) for periods N = 3S–1 < 20000 formed in finite fields GF(3S) for S = 3, 5, 7, 9 are presented. The sets include both the well–known decimation indices and the newly obtained indices that allow formatting sets of ternary Gold-like sequences (GLS) with a volume of N+2 and a low level of values of the periodic cross-correlation function. For the value S = 5, four additional indices were obtained to five known decimation indices, for S = 7, ten decimation indices were added to seven known indices, and for S = 9, nine decimation indices were additionally obtained to nine known indices.
Keywords: finite fields, primitive polynomials, correlation function, M-sequences, decimation indices
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