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Open Educational Resources (OER)

An open textbook for algebraic coding theory

This project aims to create an open textbook for teaching error-correcting codes and the beginnings of field theory. This textbook would not be very extensive, but it would contain everything needed for the 5-credit module MA3491, Fields and applications; thus incorporating the background to coding theory, the most important definitions and theorems, with proofs, and a set of exercises and computer projects that will be used for tutorials and homework assignments.

The topics covered would be:

          1. Introduction to error-correcting codes, the Hamming distance and the sphere-packing bound.

          2. A first look at finite fields.

          3.  Linear codes, in particular:
                    - The definition and basic properties.
                    - How to encode and decode when using linear codes.
                    - Check matrices and syndrome decoding.

          4. The construction of finite fields:
                    - Polynomial algebras over a field.
                    - Euclidean domains and Euclid's algorithm
                    - Unique factorization.

          5. Hamming codes.

          6. Cyclic codes.

Discipline of Mathematics - School of Mathematics, Statistics and Applied Mathematics

Authors and Partners

Dr Emil Skoldberg

Lead Author
Lecturer, NUI Galway

BSc (Mathematics and Computer science) Uppsala University, 1992. PhD (Mathematics) Stockholm University, 1997.

I have worked at NUIG since 2002, at first as a Marie Curie postdoctoral fellow, and from 2003 as lecturer in mathematics. Before that, I was a research fellow at Stockholm university between 1998 and 2002, and lecturer in mathematics at Gävle University between 1997 and 1998.
My research interests lie in algebra, particularly in combinatorial commutative algebra.

"This is a very welcome support for creating open resources in algebraic coding theory."

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Peter Phelan

Co-Author
Student, NUI Galway

 

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Milo Orlich

Co-Author
Student, Aalto University