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Multidimensional linear complexity analysis of periodic arrays

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

The linear complexity of a sequence is an important parameter for many applications, especially those related to information security, and hardware implementation. It is desirable to develop a corresponding measure and theory for multidimensional arrays that are consistent with those of sequences. In this paper we use Gröbner bases to develop a theory for analyzing the multidimensional linear complexity of general periodic arrays. We also analyze arrays constructed using the method of composition and establish tight bounds for their multidimensional linear complexity.

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Acknowledgements

Part of this work was inspired by the late Oscar Moreno. Unfortunately, he passed away before we were able to finish this paper. Sadly, co-author Francis Castro passed away before this paper was accepted for publication. We are grateful for the detailed comments given by the referee, which improved this paper greatly. The research of D. Gomez-Perez is supported by the Ministerio de Economía y Competitividad research Project MTM2014-55421-P.

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Authors and Affiliations

  1. Department of Computer Science, University of Puerto Rico, 17 Ave Universidad Ste 1701, San Juan, PR, 00925-2537, USA

    Rafael Arce-Nazario, Francis Castro, José Ortiz-Ubarri & Ivelisse Rubio

  2. Faculty of Sciences, University of Cantabria, 39071, Santander, Spain

    Domingo Gomez-Perez

  3. Gauss Research Foundation, PO Box 21613, San Juan, PR, 00931, USA

    Oscar Moreno

  4. Scientific Technology, 8 Cecil St, East Brighton, VIC, 3187, Australia

    Andrew Tirkel

Authors
  1. Rafael Arce-Nazario
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  2. Francis Castro
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  3. Domingo Gomez-Perez
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  4. Oscar Moreno
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  5. José Ortiz-Ubarri
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  6. Ivelisse Rubio
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  7. Andrew Tirkel
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Corresponding author

Correspondence to Domingo Gomez-Perez.

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Deceased: Francis Castro and Oscar Moreno.

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Arce-Nazario, R., Castro, F., Gomez-Perez, D. et al. Multidimensional linear complexity analysis of periodic arrays. AAECC 31, 43–63 (2020). https://doi.org/10.1007/s00200-019-00393-z

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  • DOI: https://doi.org/10.1007/s00200-019-00393-z

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