# 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
Autonomous Student Learning

66

Lectures

24

Tutorial

10

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 In Module Component Repeat Offered
Examination: Final Exam 2 hour End of Trimester Exam No Graded No

75

No
Examination: Mid-term exam Week 7 No Graded No

25

No

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