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# 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 or no previous experience in coding. 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 finite fields, vector spaces, bases, and linear maps. The subsequent sections demonstrate two linear codes, and these are the Parity and Hamming Codes. Also interspersed between the discussion of finite field arithmetic and linear codes are applets that demonstrate a corresponding concept or encoding method. The last section describes further research that could be added to improve this page.

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.

Next: Contents Up: Spring 2004 Final Report Previous: Spring 2004 Final Report   Contents
Frederick Leitner 2004-05-12