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This paper is dedicated to the memory of the late Oscar Moreno de Ayala. He provided the motivation and the inspiration for our study of linear complexity. We miss his presence, but his legacy lives on.Also, we thank the anonymous referees for their helpful comments. The first of the figures was done with the help of software programmed by Alvar Ibeas. During the preparation of this paper the first author was partially supported by project MTM2014-55421-P from the Ministerio de Economia, y Competitividad.

Analysis of institutional authors

Gómez Pérez, Ana IsabelAuthor

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October 18, 2022
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ARRAYS COMPOSED FROM THE EXTENDED RATIONAL CYCLE

Publicated to:Advances In Mathematics Of Communications. 11 (2): 313-327 - 2017-05-01 11(2), DOI: 10.3934/amc.2017024

Authors: Gomez-Perez, Domingo; Gomez, Ana-Isabel; Tirkel, Andrew

Affiliations

Sci Technol, 8 Cecil St, East Brighton, Vic 3187, Australia - Author
Univ Cantabria, EIIT, Avd Los Castros,S-N, Santander, Spain - Author
Univ Cantabria, Fac Ciencias, Avd Castros,S-N, Santander, Spain - Author

Abstract

We present a 3D array construction with application to video watermarking. This new construction uses two main ingredients: an extended rational cycle (ERC) as a shift sequence and a Legendre array as a base. This produces a family of 3D arrays with good auto and cross-correlation. We calculate exactly the values of the auto correlation and the cross-correlation function and their frequency. We present a unified method of obtaining multivariate recursion polynomials and their footprints for all finite multidimensional arrays. Also, we describe new results for arbitrary arrays and enunciate a result for arrays constructed using the method of composition. We also show that the size of the footprint is invariant under dimensional transformations based on the Chinese Remainder Theorem.

Keywords

Chinese remainder theoremGroebner basisLinear complexityMultidimensional arrayRecursion polynomialWatermark

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Advances In Mathematics Of Communications 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, 2017, it was in position , thus managing to position itself as a Q2 (Segundo Cuartil), in the category Computer Networks and Communications. Notably, the journal is positioned en el Cuartil Q4 for the agency WoS (JCR) in the category Mathematics, Applied.

From a relative perspective, and based on the normalized impact indicator calculated from the Field Citation Ratio (FCR) of the Dimensions source, it yields a value of: 2.41, which indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: Dimensions Jul 2025)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-07-20, the following number of citations:

  • WoS: 4

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-07-20:

  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 3 (PlumX).

It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

  • The work has been submitted to a journal whose editorial policy allows open Open Access publication.

Leadership analysis of institutional authors

This work has been carried out with international collaboration, specifically with researchers from: Australia.