Unit I

Introduction to linear codes and error correcting codes, Encoding and decoding of a linear code

Unit-II

Dual codes. Hamming codes and perfect codes.

Unit-III

Cyclic codes. Codes with Latin Squares, Introduction to BCH codes, Reed Solomon Codes

Unit-IV

Weight Enumerators and MDS codes.

Unit-V

Linear coding theory problems and conclusions.

Course Outcomes:
CO-1: To understand the basic concepts of linear/error correcting codes and apply theconcepts to encode and decode the information.
CO-2: To understand the concepts of dual /Hamming codes and apply the concept to find the parameters of given codes and their dual codes using standard matrix and polynomial operations.
CO-3: To familiarize the concepts of cyclic/BCH codes with required properties.
CO-4: To understand the concepts of weight enumerators and apply to find the weight information of the code.
To familiarize the concept of MDS code.
CO-5: Apply the basic concepts of linear codes to solve problems.

Textbooks

• Raymond Hill, A first course in Coding Theory, Clarandon Press, Oxford (1986).
• J.H. Van Lint, Introduction to Coding Theory, Springer (1998).

References

1. W. Cary Huffman and Versa Pless, Fundamentals of Error Correcting Codes, Cambridge University Press(2003).
2. W.W. Peterson, Error Correcting Codes, Cambridge, MA MIT Press (1961).
3. V. Pless, W.C. Huffman and R.A. Brualdi, An Introduction to Algebraic Codes, in Hand book of coding theory, Eds. Amsterdam Elsevier (1998).