BCH Codes

Rob Rostermundt

Date: March 30, 2002

Abstract:

Coding Theory deals with transmission of data over noisy channels. When transmitting digital data, which consists of strings of 0's and 1's, a physical device may for a number of reasons confuse these entries. For example, the Voyager II space probe which explored Jupiter in the late 1960's was transmitting data across many millions of miles with incredibly low power. When the information reached earth its easy to see how there could be errors in the data string received, either from bursts of cosmic energy or by amplification of the weak signal. To make this communication possible there needed to be a method of detecting errors in the transmission and correcting them. The process that made this possible is known as the Reed-Solomon codes. These codes are a specific type of code called a BCH code. These are the structures we wish to explore here.