The data bit enclosed by the seven regions of the Venn diagram. Let the message be the four element vector M = īy inspection, define a (4 × 7) generator matrix G in which the contents of each column correspond to The three bits to be added are three even Parity bits (P), where the parity of each is computed on different subsets of the message bits. The approach will now be generalized and studied in matrix form, where it can be extended to more powerful codes.Ĭonsider the 7-bit Hamming code built on a message having four data bits (D) which are to be transmitted as a 7-bit codeword by adding three error control bits. The examples described a linear (7,4) code in which 7-bit codewords carry 4 data bits and 3 error control bits. The Hamming Code has been introduced as a binary block code allowing correction of single bitĮrrors. Department of Electrical and Computer Engineering - University of New Brunswick, Fredericton, NB, Canada
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