# 20296 Introduction to Coding Theory 1

**Credits**: 3 intermediate credits in Mathematics or in Computer Science

**Prerequisites**: none

Required: Linear Algebra I, having accumulated a total of at least 24 credits in Mathematics, as well as the ability to read scientific texts in **English**

Recommended: Algebraic Structures

The course, based on *A First Course in Coding Theory* (4th printing), by R. Hill (Clarendon Press, 1991), was developed by Abraham Ginzburg, Mireille Avigal and Elazar Birnbaum, and includes supplementary material from chapters 1, 3, 4, 7, 9, 10 and 12 of *The Theory of Error-Correcting Codes*, by F.J. MacWilliams and N.J.A. Sloane (North-Holland, 1977).

Coding theory is a branch of Mathematics with extensive Computer Science applications. The course deals exclusively with error-correcting codes. It can serve as an introduction for students interested in the subject – whether they plan to expand their knowledge in the future or simply gain familiarity with basic concepts and results. The course requires knowledge of linear algebra and finite field theory, substantial mathematical sophistication and willingness to devote considerable time to problem solving.

**Topics**: Introduction to error-correcting codes; Finite fields; Vector spaces over finite fields; Linear codes; Encoding and decoding with a linear code; The dual code; The parity-check matrix; Syndrome decoding; The Hamming codes; Perfect codes; Codes and Latin squares; A double error-correcting decimal code; BCH codes; Cyclic codes; Reed-Solomon codes.

1Students studying towards a degree in **Mathematics** or **Computer Science**, please note: the credits for this course will be considered credits in Mathematics or in Computer Science, as necessary.