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Curricular information is subject to change
The structure of finite fields;
Knowledge of coding theoretic bounds & an ability to apply bounds to code existence;
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;
Knowledge of defining properties of classical algebraic codes, such as cyclic, Reed-Solomon and BCH codes;
Structure of cyclic codes as ideals;
Knowledge of the weight enumerator and MacWilliams duality theorem.
Principles of Error Correction: Hamming distance, sphere-packing, the main coding problem;
Linear Codes: codes as vector spaces, generator matrices, parity check matrices, the dual code, syndrome decoding;
Code Optimailty: existence bounds, operations on codes, extremal codes;
Cyclic Codes: codes as ideals in polynomial rings, generator polynomials, parity check polynomials, cyclotomic cosets;
BCH Codes: constructions from vandermonde-like matrices, connection to cyclic codes, BCH bound, Reed-Solomon codes.
Student Effort Type | Hours |
---|---|
Lectures | 24 |
Tutorial | 10 |
Total | 34 |
Not applicable to this module.
Description | Timing | Component Scale | % of Final Grade | ||
---|---|---|---|---|---|
Continuous Assessment: mid-term exam or regular assignment | Unspecified | n/a | Standard conversion grade scale 40% | No | 25 |
Examination: End of Semester Exam | 2 hour End of Trimester Exam | No | Standard conversion grade scale 40% | No | 75 |
Resit In | Terminal Exam |
---|---|
Autumn | Yes - 2 Hour |
• Group/class feedback, post-assessment
Not yet recorded.