Coding Theory

Course Description

Encoding and decoding, Vector spaces over finite fields Linear Codes, perfect codes, parity-check matrices, syndrome decoding, Hamming Codes, Cyclic Codes, BCH codes, Introduction to cryptanalysis, Exponential ciphers and public keys.

Course Objectives & Outcomes
Objectives :

• Identify mathematical principles behind coding and decoding theory.
• Use the applications of Modern Algebra.
• Discuss the theoretical aspects, algorithmic questions and applications of coding theory. 
•  Discuss the theoretical aspect of error-correcting codes use the approach of elementary enumeration, linear algebra, and finite fields.

Outcomes:
Upon successful completion of this course, the student will be able to:

• Discuss the practical applications of pure mathematics.
• Understand mathematical ideas from coding theory.
• Receive an insight in recent developments of coding theory and modern cryptography. 
•  Identify standard schemes for channel coding.
• Design codes to correct errors by using appropriate calculations. 
•  Understand the structure of specific families of BCH codes and Reed-Solomon cyclic codes as well as generalized Reed-Solomon codes

References
1. Hankerson, D.C., Hoffman, G., Leonard, D.A., Lindner, C.C., Phelps, K.T., Rodger, C.A. and Wall, J.R., 2000. Coding theory and cryptography: the essentials. CRC Press. ISBN10: 0824704657 ISBN-13: 978-0824704650.
2. Roth, R., 2006. Introduction to coding theory. Cambridge University Press. . ISBN-10: 0521845041, ISBN-13: 978-0521845045.
3. Van Lint, J.H., 2012. Introduction to coding theory (Vol. 86). Springer Science & Business Media. . ISBN-10: 0521845041, ISBN-13: 978-0521845045.
4. Ferguson, N., Schneier, B. and Kohno, T., 2010. Cryptography engineering. John Wiley & Sons. ISBN 13: 9780470474242 ISBN: 0470474246.

Course ID: MATH 551