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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
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Frederick Leitner
2004-05-12