Aspects of Coding (UMAP)

A unit using linear algebra in aspects of coding. The purpose of this module is to acquaint the undergraduate student with some of the elementary mathematical facets of coding.

Table of Contents:

1. INTRODUCTION
1.1 What is Coding?
1.2 The Coding Process
1.3 The Channel
1.4 Decoding
1.5 Shannon's Theorem

2. LINEAR CODES
2.1 The Code Concept Refined
2.2 Hamming Weight and Hamming Distance
2.3 Decoding Revisited
2.4 The Generator and Parity-check Matrices
2.5 Systematic Codes

3. ERROR CORRECTION
3.1 A Criterion for Code Quality
3.2 Error Correction and the Parity-check Matrix
3.3 Hamming Codes
3.4 Perfect Codes
3.5 The Baseball Pool Problem

4. REFERENCES

5. ANSWERS TO EXERCISES