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System of two-dimensional binary signals with ideal periodic correlation functions

I. P. Bukanov


The known strictly optimal ensembles of one-dimensional binary sequences (Gold’s, Kasami’s, sequences of bent functions) have an upper limit of the level of the periodic cross-correlation function (PCCF) considerably exceeding the zero value [1]. Therefore, of definite interest is a search for families of signals in other classes, in particular, in the case of two-dimensional binary signals, which can produce an improvement, other conditions being equal, of the upper level of the PCCF. A number of works [2–4] devoted to two-dimensional binary sequences have recently been published. However, it is necessary to note that the mathematical theory of the synthesis of such signals and systems is in the initial stage of development. A system of two-dimensional binary signals with single-level, equal to unity, PCCFs intended for use in parallel communication channels with multiple access was examined in [5]. A system with ideal, equal to zero, PCCFs is studied in the present report…

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Ipatov, V. P.; Kamaletdinov, B. Zh.; Samoilov, I.M. "Discrete sequences with good correlation properties," Zarubezhnaya Radioelektronika, No. 9, pp. 3-13, 1989.

Wild, P. "Infinite families of perfect binary arrays," Electron. Lett., Vol. 24, No. 14, p. 845-847, 1988. DOI:

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Bower, L.; Antweiler, M. "Two-dimensional perfect binary arrays with 64 elements," IEEE Trans. Information Theory, Vol. 36, No. 2, P. 411-414, 1990. DOI:

Bukanov, I. P. "A system of two-dimensional binary signals," Radioelectron. Commun. Syst., Vol. 34, No. 9, P. 70-73, 1991.



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