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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|
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||
|Examination: End of Semester Exam||2 hour End of Trimester Exam||No||Standard conversion grade scale 40%||No||
|Resit In||Terminal Exam|
|Autumn||Yes - 2 Hour|
• Group/class feedback, post-assessment
Not yet recorded.
|Lecture||Offering 1||Week(s) - 19, 20, 21, 22, 23, 24, 25, 28, 29, 30, 31, 32||Mon 09:00 - 09:50|
|Lecture||Offering 1||Week(s) - 19, 20, 21, 22, 23, 24, 25, 28, 29, 30, 31, 32||Wed 09:00 - 09:50|
|Tutorial||Offering 1||Week(s) - 19, 20, 21, 22, 23, 24, 25, 28, 29, 30, 31, 32||Fri 10:00 - 10:50|