2024/25 Undergraduate Module Catalogue

MATH3153 Coding Theory

15 creditsClass Size: 100

Module manager: Dr Rudolf Tange
Email: R.H.Tange@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2024/25

Pre-requisite qualifications

MATH2022 or MATH2080, or equivalent.

This module is not approved as a discovery module

Module summary

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.More precisely, it concerns the design of codes, i.e. sets of “meaningful words”, with good error correction and detection properties, as well as the design of efficient decoding algorithms. Error correcting codes are now widely used in applications such as wireless communication and storing data on various media.Coding theory is of considerable mathematical interest, relying on ideas from pure mathematics and demonstrating the power and elegance of algebraic techniques. Other areas of maths it is related to are Combinatorial Design Theory and Group Theory (in particular the construction of the finite simple groups).While coding theory appears to have few mathematical prerequisites, an “algebraic” mind-set is required. The student is also expected to have some knowledge of linear algebra, since most of the module will be about linear codes.

Objectives

On completion of this module, students should be able to:
a) use set theory and linear algebra to solve coding problems;
b) understand the basic notions of coding theory;
c) construct certain specific codes;
d) calculate basic properties of specific codes.

Syllabus

- Block codes and minimum distance
- Error detection and correction, and their probabilities
- Linear codes
- Coset decoding and syndrome decoding
- Hamming codes, Cyclic codes and Golay codes

Teaching methods

Delivery type	Number	Length hours	Student hours
Lecture	33	1.00	33.00
Private study hours			117.00
Total Contact hours			33.00
Total hours (100hr per 10 credits)			150.00

Private study

Studying and revising of course material.
Completing of assignments and assessments.

Opportunities for Formative Feedback

Regular problem solving assignments

Methods of assessment

Exams

Exam type	Exam duration	% of formal assessment
Standard exam (closed essays, MCQs etc)	2 hr 30 mins	100.00
Total percentage (Assessment Exams)		100.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Reading list

The reading list is available from the Library website

Last updated: 25/06/2024

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