# MAS8704 : Coding Theory

• Offered for Year: 2024/25
• Module Leader(s): Dr Stefan Kolb
• Owning School: Mathematics, Statistics and Physics
• Teaching Location: Newcastle City Campus
##### Semesters

Your programme is made up of credits, the total differs on programme to programme.

 Semester 2 Credit Value: 10 ECTS Credits: 5.0 European Credit Transfer System

#### Aims

To explain the necessity for error correcting codes, to establish their general properties, to show how to construct linear and cyclic codes and to gain practice in their use.

Module Summary
Error-correcting codes are at the heart of the digital revolution. They are used to store music on CDs and video on DVDs; to send data across telecommunications networks; and to broadcast digital television. In practice, a digital signal may be degraded in transit by many factors - cosmic rays, fluctuations in power supplies, even (in the case of a CD) dust and scratches - so that some 0s are changed to 1s and vice versa; error-correcting codes are designed to rectify this. We work with words, binary strings of some standard length n. Certain words are designated as codewords, and the signal is converted to a sequence of codewords before transmission. At the receiving end, each word is examined as it arrives, and, if it turns out to be a non-codeword (indicating that the signal has been degraded), it is replaced by the nearest codeword. This explains why small imperfections on a CD do not affect the quality of the sound that you hear. We shall concentrate on a particularly nice class of codes called linear codes, a beautiful application of elementary linear algebra. Here errors can be corrected automatically by simple matrix operations. In particular, we shall investigate cyclic codes, linear codes based on polynomials.

#### Outline Of Syllabus

General properties of codes. Perfect codes. Linear codes. Parity-check matrices and syndrome decoding. Hamming codes. Extensions of codes. Cyclic codes.

#### Teaching Methods

##### Teaching Activities
Category Activity Number Length Student Hours Comment
Guided Independent StudyAssessment preparation and completion151:0015:00Completion of in course assessments
Scheduled Learning And Teaching ActivitiesLecture51:005:00Problem classes
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision lectures
Scheduled Learning And Teaching ActivitiesLecture201:0020:00Formal lectures
Guided Independent StudyIndependent study581:0058:00Preparation time for lectures, background reading, coursework review
Total100:00
##### Jointly Taught With
Code Title
MAS3704Coding Theory
##### Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems. Tutorials are used to identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. In addition, office hours (two per week) will provide an opportunity for more direct contact between individual students and the lecturer.

#### Assessment Methods

The format of resits will be determined by the Board of Examiners

##### Exams
Description Length Semester When Set Percentage Comment
Written Examination1202A80N/A
##### Exam Pairings
Module Code Module Title Semester Comment
Coding Theory2N/A
##### Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises2M5Coursework assignments
Prob solv exercises2M5Coursework assignments
Prob solv exercises2M5Coursework assignments
Prob solv exercises2M5Coursework assignments
##### Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of the programme accreditation.

Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one ways for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.

The coursework assignments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.

Note: the exam for MAS8704 is more challenging than the exam for MAS3704.