**MATH 406**

**Introduction to Coding Theory**

**Units: 3.00**

Construction and properties of finite fields. Polynomials, vector spaces, block codes over finite fields. Hamming distance and other code parameters. Bounds relating code parameters. Cyclic codes and their structure as ideals. Weight distribution. Special codes and their relation to designs and projective planes. Decoding algorithms.

**Learning Hours:**120 (36 Lecture, 84 Private Study)

**Requirements:**Prerequisite MATH 210.

**Offering Faculty:**Faculty of Arts and Science

**Course Learning Outcomes:**

- Do matrix manipulations for linear codes and to compute decoding errors.
- Rigorously prove results on error correction and detection.
- Understand the structure of finite fields and to do computations in these fields.
- Understand various methods for encoding and decoding messages for the purpose of error-correction and to perform the necessary computations.