13912 - Coding Theory Modulübersicht

Module Number: 13912
Module Title:Coding Theory
  Datenkodierung
Department: Faculty 1 - Mathematics, Computer Science, Physics, Electrical Engineering and Information Technology
Responsible Staff Member:
  • Prof. Dr. rer. nat. Averkov, Gennadiy
Language of Teaching / Examination:English
Duration:1 semester
Frequency of Offer: On special announcement
Credits: 6
Learning Outcome:After successfully completing the module, students will know and understand the problems and basics of data coding. They can transfer known facts and procedures of linear algebra to this application field and have learned further concepts of algebra. They know linear codes and understand the meaning of the parameters. They know simple decoding algorithms, can apply them and show their correctness.
Contents:
  • Basics of coding theory
  • Theory of linear codes
  • Examples of linear codes, in particular, Reed-Solomon codes
  • General and specific decoding algorithms
  • Simple Goppa codes
Recommended Prerequisites:Knowledge of the content of the modules
  • 11101: Lineare Algebra und analytische Geometrie I
or
  • 11112: Mathematik IT-1 (Diskrete Mathematik), and
  • 11113: Mathematik IT-2 (Lineare Algebra)
Mandatory Prerequisites:None
Forms of Teaching and Proportion:
  • Lecture / 3 Hours per Week per Semester
  • Exercise / 1 Hours per Week per Semester
  • Self organised studies / 120 Hours
Teaching Materials and Literature:
  • van Lint, J., van der Geer, G., Introduction to Coding Theory and Algebraic Geometry
  • J.I. Hall, Notes on Coding Theory
  • Willems, Wolfgang, Codierungstheorie und Kryptographie
Module Examination:Final Module Examination (MAP)
Assessment Mode for Module Examination:Final module examination:
  • Written examination, 90 min. OR
  • Oral examination, 30 - 45 min. (with small number of participants)
In the first lecture it will introduced, if the examination will organized in written or oral form.
Evaluation of Module Examination:Performance Verification – graded
Limited Number of Participants:None
Part of the Study Programme:
  • Master (research-oriented) / Angewandte Mathematik / PO 2019
  • Master (research-oriented) / Artificial Intelligence / PO 2022
  • Bachelor (research-oriented) / Informatik / PO 2008 - 1. SÄ 2017
  • Master (research-oriented) / Informatik / PO 2008 - 2. SÄ 2017
  • Master (research-oriented) / Künstliche Intelligenz Technologie / PO 2022
  • Bachelor (research-oriented) / Mathematik / PO 2019
  • Bachelor (research-oriented) / Mathematik / PO 2023
  • Bachelor (research-oriented) - Co-Op Programme with Practical Placement / Mathematik - dual / PO 2023
  • Bachelor (research-oriented) / Wirtschaftsmathematik / PO 2023
  • Bachelor (research-oriented) - Co-Op Programme with Practical Placement / Wirtschaftsmathematik - dual / PO 2023
Remarks:
  • Study programme Angewandte Mathematik M.Sc.: Compulsory elective module in complex „Analysis / Algebra / Kombinatorik“
  • Study programme Mathematik B.Sc.: Compulsory elective module in complex „Vertiefung“, in limited extend 
  • Study programme Wirtschaftsmathematik B.Sc.: Compulsory elective module in complex „Vertiefung“, in limited extend
  • Study programme Artificial Intelligence M.Sc.: Compulsory elective module in complex  „Knowledge Acquisition, Representation, and Processing“
  • Study programme Informatik B.Sc.: Compulsory elective module in „Praktische Mathematik" or in field of application „Mathematics"
  • Study programme Informatik M.Sc.: Compulsory elective module in „Mathematik" or in field of application „Mathematik"
Module Components:
  • Lecture Coding Theory, with integrated exercise
  • Related examination
Components to be offered in the Current Semester: