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| Module Delivery |
Autumn semester |
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| Assessment Requirements |
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Components of Assessment
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Method(s)
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Percentage Weighting
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Coursework
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One take-home assignment and one class test
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25%
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Examination
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2 hours, unseen
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75%
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| Module Overview |
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| Prerequisites/Co-requisites |
MS113 Linear Algebra.
MS131 Probability and Statistics
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| Module Aims |
This module extends students' knowledge of linear algebra and introduces concepts of abstract algebra with rings and fields.
Applications of both linear algebra and ring theory to coding problems are considered.
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| Learning Outcomes |
By the end of the module, students should
- have an enhanced knowledge of linear algebra,
- understand the concepts of error-detecting and error-correcting codes,
- know the definitions of rings and fields, and some standard results about them,
- know how ring theory is applied to coding problems.
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| Module Content |
- Revision of vector spaces. Direct sums, orthogonal complements, quotient spaces and cosets.
- Introductory coding theory: error-correcting codes, linear codes.
- Rings, integral domains, fields. Homomorphisms. Ideals and quotient rings. Finite fields.
- Further coding theory: cyclic codes, BCH codes.
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| Methods of Teaching/Learning |
Teaching is by lectures and tutorials. Learning takes place through lectures, tutorials, exercises and class tests.
3 hours per week for 10 weeks. |
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| Selected Texts/Journals |
R. B. J. T. Allenby: Rings, Fields and Groups, Arnold (1991), ISBN. 0340544406
J. B. Fraleigh: A First Course in Abstract Algebra, Addison-Wesley (1994), ISBN 0201592916 (or later edition)
W. J. Gilbert and W. K. Nicholson: Modern Algebra with Applications, Wiley (2004),
ISBN 0471414514
Raymond Hill: A First Course in Coding Theory, Oxford (1990), ISBN 0198538030
Paul Garrett: The Mathematics of Coding Theory, Pearson (2004), ISBN 0131019678.
L.R. Vermani: Elements of Algebraic Coding Theory, Chapman & Hall / CRC (1996), ISBN 0412573806 |
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| Last Updated |
27 August 2007 |
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