Reference for citation: Grigoriev Е. К., Sergeev А. М. Formation of ensembles of quasi-orthogonal code sequences with high structural secrecy. Journal of Instrument Engineering. 2025. Vol. 68, N 5. P. 388–396 (in Russian). DOI: 10.17586/0021-3454-2025-68-5-388-396.

Abstract. One of the possible directions of increasing the noise immunity of systems using the direct sequence method for spectrum spreading is investigated, namely, a change in the paradigm that assumes that code sequences should be binary and symmetric, in favor of non-binary and asymmetric sequences. An approach to the formation of ensembles of quasi-orthogonal code sequences with high structural secrecy is presented. The specified characteristics are achieved through the analysis of known Gordon — Mills — Welch (GMW) code sequences with good correlation properties and high structural secrecy based on the theory of quasi-orthogonal matrices. These sequences are the basis for constructing cyclic Mersenne matrices with elements {1, –b}. The prototype, the GMW sequence, is modified by replacing the element “0” with the element “–b”, which is calculated in accordance with the theory of quasi-orthogonal matrices. Autocorrelation and intercorrelation functions are calculated for the resulting ensemble. It is shown that quasi-orthogonality of the sequence ensemble being formed is achieved, and at the same time the correlation properties are not worsened in comparison with the prototype. The obtained results have both independent significance and can be a component of the algorithms for generating GMV sequences.

Keywords: quasi-orthogonal matrices, correlation function, structural secrecy, Hadamard matrices, Mersenne matrices, Gordon — Mills — Welch sequences

Acknowledgement: The work was carried out with the financial support of the Ministry of Science and Higher Education of the Russian Federation, agreement No. FSRF-2023-0003 “Fundamental principles for constructing noise-resistant systems of space and satellite communications, relative navigation, technical vision and aerospace monitoring”.

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