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Solving Shift Register Problems over Skew Polynomial Rings using Module Minimisation

W Li 1 Johan Sebastian Rosenkilde Nielsen 2 S Puchinger 1 V Sidorenko 1
1 INT - University of Ulm. - Institute of Communications Engineering [Ulm]
2 GRACE - Geometry, arithmetic, algorithms, codes and encryption
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
Abstract : For many algebraic codes the main part of decoding can be reduced to a shift register synthesis problem. In this paper we present an approach for solving generalised shift register problems over skew polynomial rings which occur in error and erasure decoding of L-interleaved Gabidulin codes. The algorithm is based on module minimisation and has time complexity O(L*mu^2) where mu measures the size of the input problem.
Keywords : Skew Polynomials Ore Polynomials Shift Register Synthe-sis Module Minimisation Gabidulin Codes
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https://hal.inria.fr/hal-01245068
Contributor : Johan S. R. Nielsen <>
Submitted on : Wednesday, December 16, 2015 - 4:08:24 PM
Last modification on : Monday, June 15, 2020 - 10:50:02 PM
Long-term archiving on: : Saturday, April 29, 2017 - 4:55:10 PM

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  • HAL Id : hal-01245068, version 1
  • ARXIV : 1501.04797

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INRIA | UNIV-PARIS-SACLAY | LIX | X-LIX | X | X-DEP-INFO | CNRS

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W Li, Johan Sebastian Rosenkilde Nielsen, S Puchinger, V Sidorenko. Solving Shift Register Problems over Skew Polynomial Rings using Module Minimisation. International Workshop on Coding and Cryptography 2015, Apr 2015, Paris, France. ⟨hal-01245068⟩

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