Mathematics

Coding Theory

Module code: 855G1
Level 7 (Masters)
15 credits in spring teaching
Teaching method: Lecture
Assessment modes: Unseen examination, Coursework

Topics covered include: 

  • Introduction to error-correcting codes. The main coding theory problem. Finite fields.
  • Vector spaces over finite fields. Linear codes. Encoding and decoding with a linear code.
  • The dual code and the parity check matrix. Hamming codes. Constructions of codes.
  • Weight enumerators. Cyclic codes. MDS codes.

Module learning outcomes

  • Calculate the fundamental parameters of a code. Find a generator matrix and a parity-check matrix. Encode and decode. Understand Hamming, cyclic and MDS codes.