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\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Huffman and Hamming codes. The left column shows the sixteen possible 4-bit messages, the other columns show the encoded version of each message. The Huffman code is for data compression: the most likely messages have the shortest encoded forms; the code is given for the case that each message bit is three times more likely to be zero than one. The Hamming code is an error correcting code: every codeword differs from all the others in at least 3 places, therefore any single error can be corrected. The Hamming code is also linear: all the words are given by linear combinations of $1010101,\mskip \thickmuskip 0110011,\mskip \thickmuskip 0001111,\mskip \thickmuskip 1111111$. They satisfy the parity checks $1010101,\mskip \thickmuskip 0110011,\mskip \thickmuskip 0001111$.}}{65}}