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