Solving Shift Register Problems over Skew Polynomial Rings using Module Minimisation

W. Li, Johan Sebastian Rosenkilde Nielsen, S. Puchinger, V. Sidorenko

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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 2) where U measures the size of the input problem.
Original languageEnglish
Publication date2015
Number of pages10
Publication statusPublished - 2015
Externally publishedYes
Event9th International Workshop on Coding and Cryptography (WCC 2015) - Paris, France
Duration: 13 Apr 201517 Apr 2015
Conference number: 9
http://wcc2015.inria.fr/

Conference

Conference9th International Workshop on Coding and Cryptography (WCC 2015)
Number9
CountryFrance
CityParis
Period13/04/201517/04/2015
OtherOrganized by INRIA
Internet address

Keywords

  • Skew Polynomials
  • Ore Polynomials
  • Shift Register Synthesis
  • Module Minimisation
  • Gabidulin Codes

Cite this

Li, W., Nielsen, J. S. R., Puchinger, S., & Sidorenko, V. (2015). Solving Shift Register Problems over Skew Polynomial Rings using Module Minimisation. Paper presented at 9th International Workshop on Coding and Cryptography (WCC 2015), Paris, France.