MATB24H3 Lecture Notes - Parity-Check Matrix, Hamming Weight, Generator Matrix

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21 Apr 2013
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In this application messages will be encoded using the binary alphabet {0, 1} : b will be used to create message words that will be encoded, transmitted, received and then decoded. The hamming 7-4 code starts with messages" that have length 4 each rep. a letter. i. e. all possible messages: 24 = 16. space. To simply send these is simple but if an error occurs then it cannot be detected. i. e. say message received is 1 which decodes to the word bean but the correct message is. There is one mistake in each of the words. We want to detect single-error transmissions and to correct, the error. To do these we lengthen the words to have 7 characters where the last 3. Check" for errors. i. e. if x1, x2, x3, x4 are the rst 4 characters and the last 3 are given by equations carefully chosen.

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