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A linear algebraic approach to multisequence shift-register synthesis

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Abstract

An efficient algorithm which synthesizes all shortest linear-feedback shift registers generating K given sequences with possibly different lengths over a field is derived, and its correctness is proved. The proposed algorithm generalizes the Berlekamp-Massey and Feng-Tzeng algorithms and is based on Massey’s ideas. The time complexity of the algorithm is O(KλN) ≲ O(KN 2), where N is the length of a longest sequence and λ is the linear complexity of the sequences.

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Authors and Affiliations

  1. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

    V. R. Sidorenko

  2. Ulm University, Ulm, Germany

    V. R. Sidorenko

  3. Esslingen University of Applied Sciences, Esslingen, Germany

    G. Schmidt

Authors
  1. V. R. Sidorenko
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  2. G. Schmidt
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Correspondence to V. R. Sidorenko.

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Original Russian Text © V.R. Sidorenko, G. Schmidt, 2011, published in Problemy Peredachi Informatsii, 2011, Vol. 47, No. 2, pp. 72–89.

Supported in part by the German Research Council (DFG), project nos. BO 867/14 and BO 867/21-1.

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Sidorenko, V.R., Schmidt, G. A linear algebraic approach to multisequence shift-register synthesis. Probl Inf Transm 47, 149–165 (2011). https://doi.org/10.1134/S0032946011020062

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