Lecture Notes

Here you can download the lecture notes of Algebraische Codierung für die sichere Datenübertragung,
a lecture I hold from Wintersemester 2005/2006 for ten years until Wintersemester 2014/2015 at Ruhr-University Bochum. It is in German.

Overview: This very short overview contains some general literature recommendations, a couple of keywords, and the special literature used for the lecture: Overview

The lecture treats algebraic coding from an engineering point of view. Its main advantage is that it comes quite fast to the point and includes coding- as well as decoding algorithms for the most important code classes. It also covers non-Hamming metrics. First the Lee distance, where a simple derivation of Roth's algorithm for decoding negacyclic codes is included (see also here for a short english summary). Second the Mannheim Distance which does the same on a finite two-dimensional grid what the Lee distance does on the circle (the Mannheim distance was introduced in my article K.Huber, "Codes over Gaussian Integers", IEEE Trans. on Inf. Theory, Vol.40, No.1, January 1994, pp.207-216). The Mannheim distance is interesting for coding over QAM-Signalconstellations (see also here and entries [17],[24],[25] in my publication list).

The lectures have exercises at the end. The solutions of these exercises are given at the end of the subsequent lecture. If you follow the lectures and work through the exercises you will be able to implement coding- and decoding algorithms for BCH-, RS-, and Goppa Codes.

Lecture 1: Vorlesung 17.10.2014 size 4.5 MB (Basics, Generator-, Paritycheckmatrices, Singleton-, Hammingbounds, Finite Fields, Euclidean Algorithm)

Lecture 2: Vorlesung 31.10.2014 size 3.4 MB (Generatorpolynomial, Minimalpolynomials, Two-Error Correcting Codes, Solving quadratic equations over GF(2^m), BCH-Codes)

Lecture 3: Vorlesung 14.11.2014 size 5.5 MB (BCH-Codes, RS-Codes, Decoding of BCH- and RS-Codes)

Lecture 4: Vorlesung 28.11.2014 size 3.4 MB (Goppa Codes, Decoding of Goppa Codes)

Lecture 5: Vorlesung 12.12.2014 size 3.8 MB (Goppa Codes, McEliece Cryptosystem, Codes for non-Hamming distances, negacyclic Codes)

Lecture 6: Vorlesung 09.01.2015 size 4.7 MB (Decoding of negacyclic Codes, Berlekamp's Algorithm, Roth's algorithm, Mannheim distance, icyclic Codes, MacWilliam's transform)

Lecture 7: Vorlesung 23.01.2015 size 0.9 MB

Exam 2009: Prüfung 06.03.2009

Exam 2010: Prüfung 02.03.2010

Exam 2011: Prüfung 23.03.2011

Exam 2012: Prüfung 07.03.2012

Exam 2013: Prüfung 07.03.2013

Exam WS 2014: Prüfung 20.02.2014

Exam SS 2014: Prüfung 31.07.2014

Exam WS 2015: Prüfung 19.02.2015

Exam SS 2015: Prüfung 07.08.2015