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The authors want to thank Andrew Tirkel for the useful discussions and pointing to the problem. Domingo GomezPerez, Ana I. Gomez and Francisco-Javier Soto and partially supported by Research Project "PROTOCOLOS SEGUROS EN REDES DESCENTRALIZADAS.(AYUDA FINANCIADA CONTRATO PROGRAMA GOB CANTABRIA - UC)". In addition, Francisco-Javier Soto acknowledges support from the "PREDOCT2022-006" of Univerdidad Rey Juan Carlos.

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Gomez, Ana, IAuthor

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A new family of binary sequences based on the generalized ERC construction

Publicated to:Ieee International Symposium On Information Theory - Proceedings. 1327-1331 - 2024-01-01 (), DOI: 10.1109/ISIT57864.2024.10619519

Authors: Soto, Francisco-Javier; Gomez, Ana, I; Gomez-Perez, Domingo

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Abstract

Families of binary sequences with good auto- or cross-correlation properties are required in areas such as cryptography, wireless communications, and digital watermarking. Algebraic constructions present an advantage over random sequences in that fixed bounds can be provided for the off-peak correlation. The interleave and the composition method take a well-distributed pseudonoise sequence, such as an m-sequence, that can be extended to produce larger families with given properties and longer periods. The interleave method or row-by-row folding of a sequence is a popular approach to generate families such as Gordon Mill Welch (GMW) sequences, which are constructed using a shift sequence with good correlation properties. The method of composition (a different approach) also requires a shift sequence and a pseudonoise sequence to construct a new family more related with multidimensional periodic arrays. In this work, we develop new families of binary sequences with good pseudorandom properties based on both the interleave and composition methods, which offer flexible periods and easy implementation. This new construction is based on the generalized Extended Rational Cycle (ERC) construction developed by Rivat and Niederreiter. The results show that for certain parameters the obtained families are close to optimal in terms of family size and correlation.

Keywords

Applied mathematicsInformation systemsModeling and simulationTheoretical computer science

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Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Ieee International Symposium On Information Theory - Proceedings due to its progression and the good impact it has achieved in recent years, according to the agency Scopus (SJR), it has become a reference in its field. In the year of publication of the work, 2024 there are still no calculated indicators, but in 2023, it was in position , thus managing to position itself as a Q2 (Segundo Cuartil), in the category Modeling and Simulation.

Leadership analysis of institutional authors

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author () .

the author responsible for correspondence tasks has been .