MATH30180 An Intro to Coding Theory

Academic Year 2023/2024

Error correcting codes play a central role in all areas of communications technology such as deep space communication, mobile telephony and digital storage.

This is intended as an introduction to algebraic coding theory. The approach uses principles of linear algebra, groups, rings and finite fields and applied them to the study of error-correcting codes. Questions of code constructions, existence and fundamental theorems will be addressed, all in respect of the Hamming metric. Several well-known families of codes will be studied.

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Curricular information is subject to change

Learning Outcomes:

Knowledge of coding theoretic bounds & an ability to apply bounds to code existence questions;
An understanding of codes as vector spaces, the dual code, generator and parity check matrices;
Knowledge of the principles of error correction, working knowledge of syndrome decoding and its complexity;
An understanding of code optimality and extremality;
Understanding of code equivalence;
Knowledge of fundmental operations on codes such as puncturing, shortening, and extending;
Knowledge of defining properties of classical algebraic codes, such as cyclic, Reed-Solomon and BCH codes;
Structure of cyclic codes as ideals;

Student Effort Hours: 
Student Effort Type Hours
Lectures

24

Tutorial

10

Autonomous Student Learning

66

Total

100

Approaches to Teaching and Learning:
lectures; tutorials, problem-based learning, group work; 
Requirements, Exclusions and Recommendations

Not applicable to this module.


Module Requisites and Incompatibles
Pre-requisite:
MATH20300 - Linear Algebra 2 (MathSci), MATH20310 - Groups, Rings and Fields, MST20050 - Linear Algebra II, MST30010 - Group Theory and Applications


 
Assessment Strategy  
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade
Examination: Mid-term exam Week 7 No Graded No

25

Examination: Final Exam 2 hour End of Trimester Exam No Graded No

75


Carry forward of passed components
No
 
Resit In Terminal Exam
Autumn Yes - 2 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 
Feedback Strategy/Strategies

• Group/class feedback, post-assessment

How will my Feedback be Delivered?

Not yet recorded.

C. Huffman, V. Pless, Fundamentals of Error-Correcting Codes, Cambridge,
Name Role
Beatriz Barbero Lucas Tutor
Mr Lucien Francois Tutor
Timetabling information is displayed only for guidance purposes, relates to the current Academic Year only and is subject to change.
 
Spring
     
Lecture Offering 1 Week(s) - 20, 21, 22, 23, 24, 25, 26, 29, 30, 32, 33 Mon 09:00 - 09:50
Lecture Offering 1 Week(s) - 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 Wed 09:00 - 09:50
Tutorial Offering 1 Week(s) - 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 Fri 11:00 - 11:50
Spring