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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 
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.
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Submitted on : Wednesday, December 16, 2015 - 4:08:24 PM
Last modification on : Wednesday, February 2, 2022 - 3:58:06 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


W Li, Johan Sebastian Rosenkilde Nielsen, S Puchinger, V Sidorenko. Solving Shift Register Problems over Skew Polynomial Rings using Module Minimisation. WCC2015 - 9th International Workshop on Coding and Cryptography 2015, Anne Canteaut, Gaëtan Leurent, Maria Naya-Plasencia, Apr 2015, Paris, France. ⟨hal-01245068⟩



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