Singapore University of Social Sciences

Coding Theory

Coding Theory (MTH351)


MTH351 Coding Theory introduces students to mathematics behind successful transmission of data through a noisy channel and correcting errors in corrupted messages. The topics covered are of central importance for many applications in computer science and engineering. The course gives a comprehensive introduction to coding theory whilst only assuming basic linear algebra. The issues of bounds and decoding essential to the design of good codes will be featured prominently.

Level: 3
Credit Units: 5
Presentation Pattern: Every July


  • Groups
  • Cosets
  • Polynomial Rings
  • Fields
  • Finite Fields
  • Linear Codes
  • Hamming Distances and Hamming Codes
  • Cyclic Codes
  • BCH Codes
  • Reed-Solomon Codes
  • Goppa Codes
  • Turbo Codes

Learning Outcome

  • Show the existence/non-existence of certain codes with certain parameters.
  • Demonstrate the decoding of BCH codes, Reed-Solomon codes and Quadratic-residue codes.
  • Calculate generator matrix and parity-check matrix of a given linear code.
  • Construct certain linear codes from other given linear code.
  • Determine the generator polynomial of a given cyclic code.
  • Compute the capacity of a discrete memoryless communications channel.
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