15BCE0375_EXP-2_HAMMING_CODE.docx

# 15BCE0375_EXP-2_HAMMING_CODE.docx - ERROR DETECTION...

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ERROR DETECTION & CORRECTION USING HAMMING CODE NAME: SINGU SAI VARUN TEJA CHOWDARY REG.NO: 15BCE0375 SLOT: L9+L10 FACULTY: JAISANKAR N TASK: ERROR DETECTION & CORRECTION USING HAMMING CODE DESCRIPTION: Hamming codes are a class of binary linear codes. For each integer r ≥ 2 there is a code with block length n = 2 r − 1 and message length k = 2 r − r − 1 . Hence the rate of Hamming codes is R = k / n = 1 − r / (2 r − 1) , which is the highest possible for codes with minimum distance of three (i.e., the minimal number of bit changes needed to go from any code word to any other code word is three) and block length 2 r − 1 . The parity-check matrix of a Hamming code is constructed by listing all columns of length r that are non-zero, which means that the dual code of the Hamming code is the shortened Hadamard code. The parity-check matrix has the property that any two columns are pairwise linearly independent. ALGORITHM/PSUEDOCODE: 1. Number the bits starting from 1: bit 1, 2, 3, 4, 5, etc.

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• Fall '17
• jaa

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