Reference for citation: Starodubtsev V. G., Morozov Y. G. Sets of quinary Kasami-like sequences for digital information transmission systems. Journal of Instrument Engineering. 2024. Vol. 67, N 8. P. 637–646 (in Russian). DOI: 10.17586/0021-34542024-67-8-637-646.

Abstract. For quinary basic M-sequences (MS) with the period N = 5S – 1 (S = 4, 6), sets of vectors of decimation indices IS,MK = (d1, d2, ..., dn) are presented, on the basis of which small sets of Kasami-like sequences (KLS) with the period N < 20 000 are formed in the finite fields GF(5S). It is shown that for values of S = 4, 6 the periodic cross-correlation function (PCCF) of a small set of KLS is four-level with a maximum value of the PCCF RmaxS,MK = (5S/2 + 1). The values of the volumes of small sets of quinary KLS are given.

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

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