Solving Shift Register Problems over Skew Polynomial Rings using Module Minimisation

W Li; Johan Sebastian Rosenkilde Nielsen; S Puchinger; V Sidorenko

Conference papers

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 : Shift Register Synthe-sis Ore Polynomials Skew Polynomials Module Minimisation Gabidulin Codes

Document type :

Conference papers

Domain :

Computer Science [cs] / Information Theory [cs.IT]

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https://hal.inria.fr/hal-01245068
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Submitted on : Wednesday, December 16, 2015 - 4:08:24 PM
Last modification on : Monday, July 26, 2021 - 11:06:59 AM
Long-term archiving on: : Saturday, April 29, 2017 - 4:55:10 PM

Solving Shift Register Problems over Skew Polynomial Rings using Module Minimisation

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