# Singapore University of Social Sciences

## Coding Theory (MTH351)

Applications Open: 01 April 2020

Applications Close: 31 May 2020

Next Available Intake: July 2020

Language: English

Duration: 6 months

Fees: \$1378 View More Details on Fees

Area of Interest: Science & Technology

Schemes: Alumni Continuing Education + (ACE+), Lifelong Learning Credit (L2C), Resilience 2020

Funding: SkillsFuture

School/Department: School of Science & Technology

### Synopsis

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

### Topics

• 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.