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Designs, Codes and Cryptography

, Volume 87, Issue 2–3, pp 589–607 | Cite as

Improved power decoding of interleaved one-point Hermitian codes

  • Sven PuchingerEmail author
  • Johan Rosenkilde
  • Irene Bouw
Article
  • 59 Downloads
Part of the following topical collections:
  1. Special Issue: Coding and Cryptography

Abstract

An \(h\)-interleaved one-point Hermitian code is a direct sum of \(h\) many one-point Hermitian codes, where errors are assumed to occur at the same positions in the constituent codewords. We propose a new partial decoding algorithm for these codes that can decode—under certain assumptions—an error of relative weight up to \(1-\big (\tfrac{k+g}{n}\big )^{\frac{h}{h+1}}\), where k is the dimension, n the length, and g the genus of the code. Simulation results for various parameters indicate that the new decoder achieves this maximal decoding radius with high probability. The algorithm is based on a recent generalization of improved power decoding to interleaved Reed–Solomon codes, does not require an expensive root-finding step, and improves upon the previous best decoding radius at all rates. In the special case \(h=1\), we obtain an adaption of the improved power decoding algorithm to one-point Hermitian codes, which for all simulated parameters achieves a similar observed failure probability as the Guruswami–Sudan decoder above the latter’s guaranteed decoding radius.

Keywords

Interleaved one-point Hermitian codes Power decoding Collaborative decoding 

Mathematics Subject Classification

94B35 14G50 

Notes

Acknowledgements

We would like to thank the anonymous reviewers for their helpful comments, which improved the readability of the paper.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute for Communications EngineeringTechnical University of MunichMunichGermany
  2. 2.Department of Applied Mathematics and Computer ScienceTechnical University of DenmarkKgs. LyngbyDenmark
  3. 3.Institute of Pure MathematicsUlm UniversityUlmGermany

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