RTG – Coding Theory, Cryptography and Number Theory
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  • Home
  • People
    • Faculty
    • Students
  • Undergraduate
    • GRE Preparation
    • Preparation for REU
      • Preparation for REU 2020
      • Preparation for REU 2019
      • Preparation for REU 2018
      • Preparation to REU 2017
    • REU
      • REU 2020
      • REU 2019
      • REU 2018
      • REU 2017
    • Creative Inquiry
  • Graduate
    • Path to Research Readiness
    • Algebra Prelim Preparation
    • Advanced teaching experience
  • Research
    • Early Career Research Workshop in Coding Theory, Cryptography, and Number Theory
      • 2019 ECRW
      • 2018 ECRW
    • Reading and working groups
    • RTG – Coding, Cryptography and Number Theory (CCNT) Seminar
    • Shannon Centennial at Clemson
  • Media archives
    • News
    • RTG seminar videos
      • 2016-2017
      • 2017-2018
      • 2018-2019
    • Lecture series videos
      • 2016/17: Nigel Boston
      • 2017/18: Gauri Joshi
      • 2018/19: Elisa Gorla
    • Other seminars videos

Other seminars videos

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  • 10/18/2016 – AGNT Seminar
    Anna-Lena Horlemann – EPF Lausanne
    Linearized polynomial modules and their application to network coding – video
    Linearized polynomials are a certain family of polynomials over finite fields. They form a non-commutative ring with the two operations addition and composition. In this ring we will consider special modules of rank 2, which we call interpolation modules, and determine minimal (Gröbner) bases of these modules. Furthermore we give a brief introduction to network coding and show how linearized polynomials are used to construct optimal rank-metric codes, also called Gabidulin codes. In the network coding setting, the problem of decoding such a code can be translated to a parametrization based on a minimal basis of the interpolation module. We conclude our talk by explaining the parametrization and the decoding algorithm, and determining the complexity order of it.

Supported by the National Science Foundation (NSF) under Grant No. DMS:1547399. Any opinions, findings and conclusions or recommendations expressed in these materials are those of the authors and do not necessarily reflect the views of NSF.