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Coding Theory Case Study

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Coding Theory Case Study
James Sole
UoP / MTH/221
Michael Wiemann
10/25/2014

Abstract
This paper will explore the uses of a Coding Theory Case Study and how it can be used in a real world application. This paper will go into depth about Error Detecting Codes, Error Correcting Codes, Hamming Distances, Perfect Codes, Generator Matrices, Parity Check Matrices, and Hamming Codes and the role these play in determining a Coding Theory Case Study. Throughout this paper, each part of a Coding Theory Case Study will be examined and how a viable example can use these parts to complete the requirements of a real world application.

Coding Theory Case Study
When it comes to representing, manipulating and transferring information, the usual way of doing it is to use what is called bit strings which consist of zeroes and ones. The prevention of errors when storing data or retrieving data is extremely difficult, if not impossible due to any number of external factors, be it human error, electrical failure, or equipment failure. This paper will explore and detail how techniques from code theory are used to ensure data is transmitted reliably and the recovery of data that may have been lost due to a number of factors.
Error Detecting Codes
When data errors occur, be it corrupted stored data or the corruption of data being transferred, error detecting codes play a huge role in how errors can be detected and ultimately corrected. A simple way to detect errors when a bit string is transmitted is to add a parity check bit at the end of the string (Rosen, 2012). When working with a parity check bit, there are two options available, the first being that if a bit string contains an even number of 1s, one would put a zero at the end of the string, while if the bit string contains an odd number of 1s, one would put a 1 at the end of the string. A formula that exists for this specific function is x1x2… xn as x1 x2… xnxn+1 where the parity check bit xn+1 is given by...

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