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Grant support

The authors want to thank Prof. Arne Winterhof for pointing out a better bound in Theorem 5 and other valuable comments that greatly improved the work. Thanks also go to the anonymous referee for their careful reviewing and valuable comments. Z. Chen was partially supported by the National Natural Science Foundation of China under grant No. 61772292, and by the Provincial Natural Science Foundation of Fujian, China under grant No. 2020J01905. D. Gomez-Perez and A. I. Gomez are supported by the Spanish Agencia Estatal de Investigacion project Secuencias y curvas en criptografia (Project PID2019-110633GB-I00 founded by MCIN/AEI/10.13039/501100011033) .

Analysis of institutional authors

Gomez-Perez, DCorresponding Author

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September 27, 2022
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Correlation measure, linear complexity and maximum order complexity for families of binary sequences

Publicated to:Finite Fields And Their Applications. 78 (101977): 101977- - 2022-02-01 78(101977), DOI: 10.1016/j.ffa.2021.101977

Authors: Chen, Zhixiong; Gomez, Ana, I; Gomez-Perez, Domingo; Tirkel, Andrew

Affiliations

Putian Univ, Key Lab Appl Math, Fujian Prov Univ, Putian 351100, Fujian, Peoples R China - Author
Sci Technol, 8 Cecil St, Melbourne, Vic 3187, Australia - Author
Univ Cantabria, Dept Math Stat & Comp Sci, Santander, Spain - Author
Univ Rey Juan Carlos, Dept Comp Sci, Madrid, Spain - Author

Abstract

The correlation measure of order k is an important measure of pseudorandomness for binary sequences. This measure tries to look for dependence between several shifted versions of a sequence. We study the relation between the correlation measure of order k and two other pseudorandom measures: the Nth linear complexity and the Nth maximum order complexity. We simplify and improve several state-of-the-art lower bounds for these two measures using the Hamming bound as well as weaker bounds derived from it. (C) 2021 Elsevier Inc. All rights reserved.

Keywords

Binary sequencesComputational complexityCorrelation measure of order kCorrelation measuresLinear complexityLow boundNth linear complexityNth maximum order complexityPseudo-randomPseudorandomPseudorandom sequencesPseudorandomnessState of the artTriple correlation-analysis

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Finite Fields And Their Applications 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, 2022, it was in position , thus managing to position itself as a Q1 (Primer Cuartil), in the category Algebra and Number Theory. Notably, the journal is positioned above the 90th percentile.

From a relative perspective, and based on the normalized impact indicator calculated from World Citations provided by WoS (ESI, Clarivate), it yields a value for the citation normalization relative to the expected citation rate of: 3.38. This 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: ESI Nov 14, 2024)

This information is reinforced by other indicators of the same type, which, although dynamic over time and dependent on the set of average global citations at the time of their calculation, consistently position the work at some point among the top 50% most cited in its field:

  • Field Citation Ratio (FCR) from Dimensions: 9.79 (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: 9
  • Scopus: 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:

With a more dissemination-oriented intent and targeting more general audiences, we can observe other more global scores such as:

  • The Total Score from Altmetric: 1.85.
  • The number of mentions on the social network X (formerly Twitter): 2 (Altmetric).

Leadership analysis of institutional authors

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

the author responsible for correspondence tasks has been Gómez Pérez, Ana Isabel.