2005/06 Undergraduate Module Catalogue

MATH3152 Coding Theory

10 creditsClass Size: 200

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2005/06

Pre-requisites

MATH1011 or MATH1330 or MATH2080 or equivalent.

This module is approved as an Elective

Objectives

To provide an introduction to linear codes in particular and coding in general, discussing the merits of various methods. On completion of this module, students should be able to: (a) demonstrate the basic theory of codes; (b) construct certain specific codes; (c) calculate basic properties of specific codes.

Syllabus

The subject of error correcting codes is modern, starting with an article by Shannon in 1948. It concerns the practical problem of ensuring reliable transmission of digital data through a noisy channel. Error correcting codes are now widely used in applications such as transmitting satellite pictures, designing registration numbers and storing data on magnetic tapes and CD's. The theory is of considerable mathematical interest, relying on ideas from pure mathematics and demonstrating the power and elegance of algebraic techniques. Some or all of: 1. Error correcting codes. Hamming distance, elementary examples. 2. Algebraic preliminaries. Linear algebra, finite fields. 3. Algebraic coding theory. Cyclic codes, dual codes, quadratic residue and BCH codes. 4. Steiner systems. Golay codes. 5. Information theory. Entropy and Shannon's theorem. 6. Variable length codes. Huffman codes.

Teaching methods

Lectures: 20 hours. 6 examples classes.

Methods of assessment

One 2 hour examination at end of semester (100%).

Reading list

The reading list is available from the Library website

Last updated: 13/05/2005

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