Preface

Purpose This web page is designed as a tutorial for students who want to learn about error checking and linear block codes, but who may not have a strong background in linear algebra and limited previous experience in coding. This tutorial is an extension of the report of the same name written in Spring 2004. The following sections will give a brief tutorial in the mathematical concepts needed to understand the workings of linear codes. There will be different sections dedicated to hamming codes, parity codes, cyclic codes, and these codes' java implementation. The first few sections will outline the matrix operation classes used as a starting point before developing the linear code classes. The final result of this report will be two applets, one which can encode webpages with the described linear codes, and a second which will display the generating and parity check matrices for each code.

A Brief Introduction The real-world applications of error checking and linear block codes are in digital data transfer. Typical communication channels include telephone lines, high-frequency radio links, microwave links, satellite links, semi-conductor memories, and magnetic tapes. Data is encoded to be transferred over these channels. Linear block codes are used to encode the data. In many situations the encoded data can be corrupted during transfer. Corruption occurs when there is noise on the line or some physical disturbance interrupts the data. If the data does not arrive in perfect condition, error-checking codes are required to find the errors in the data and possibly fix these errors. Describing the different error-checking codes involves finite field arithmetic.