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11
Issue
vol 62 / November, 2019
Article

DOI 10.17586/0021-3454-2016-59-3-202-210

UDC 519.725

GENERATION OF TERNARY GORDON—MILLS—WELCH SEQUENCES ON THE BASE OF SHIFT REGISTERS

V. G. Starodubtsev
Multiservice Nets and Telecommunications, Ltd., St. Petersburg; Head of Department


A. E. Chernyavskikh
A. F. Mozhaysky Military Space Academy, Department of Technologies and Means of Complex Processing and Transfer of Information in Automated Control Systems; Student


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Abstract. An algorithm for the generation of ternary Gordon—Mills—Welch (GMW) sequences and for determining the initial states of the shift registers, incorporated into the generation device, is developed. Ternary GMW-sequences, as well as binary, may be formed on the base of set of shift registers, which linear feedback are determined by coefficients of indivisible polynomials being the factors of testing polynomials of GMW-sequences. The main problem in the construction of devices generating ternary GMWsequences based on shift registers is absence in literature of algorithms of definition of their initial states. In accordance with the proposed algorithm the initial state of shift registers is determined by the decimation of the symbols of the base M-sequence, on which GMW-sequence is formed. Decimation index depends on the ratio of the degrees of the roots of polynomials-factors and roots of polynomial of the base M-sequence.
Keywords: ternary sequences of composite period, finite fields, indivisible and primitive polynomials, shift register with linear feedback

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