## 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 2023/24

### Pre-requisite qualifications

MATH2020 or MATH2022 or MATH2080, or equivalent.

### This module is mutually exclusive with

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. Error correcting codes are now widely used in applications such as transmitting satellite pictures, designing registration numbers and storing data on various media.The theory is of considerable mathematical interest, relying on ideas from pure mathematics and demonstrating the power and elegance of algebraic techniques.Note that while coding theory appears to have few mathematical prerequisites, an 'algebraic' mind-set is required.

### Objectives

On completion of this module, students should be able to:
a) understand the idea of deployment of set theoretic organisational tools to solve complex practical problems;
b) demonstrate the basic theory of codes;
c) construct certain specific codes;
d) calculate basic properties of specific codes.

### Syllabus

- Algebraic preliminaries (linear algebra, fields)
- Theory of Coding
- Block codes (e.g. Hamming Codes, Cyclic Codes)
- Information theory
- Variable length 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