Reference for citation: Starodubtsev V. G., Chetverikov E. A. Formation of sets of ternary Kasami-like sequences for digital information transmission systems. Journal of Instrument Engineering. 2023. Vol. 66, N 10. P. 807—817 (in Russian). DOI: 10.17586/0021-3454-2023-66-10-807-817.

Abstract. Sets of vectors of decimation indices IS(id1, id2, ..., idn) of ternary M-sequences are presented, on the basis of which small and large sets of Kasami-similar sequences (KSS) with periods N = 3S–1< 20000 are formed in finite fields GF(3S) (S = 4, 6, 8). It is shown that for even values of S, the periodic cross-correlation function of a small set of KSS is three-level with the maximum value of the module of the mutual correlation function Rmax = (3S/2+1)). The correlation function of a large set at S=4 is eight-level with Rmax = (2·3S/2+1), and at S = 6, 8 is ten-level with Rmax = (3S/2+1+1). The values of the volumes of small and large sets of ternary KSS are given.

Keywords: finite fields, correlation function, M-sequences, Kasami sequences, decimation indices

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