Any linear code can be transformed into an equivalent

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Unformatted text preview: little redundancy can we get away with and still manage to correct errors? The Hamming code uses a clever construction that uses the intuition developed while answering the question mentioned above. We answer this question next. ￿ 6.4.2 How many parity bits are needed in a SEC code? Let’s think about what we’re trying to accomplish with a SEC code: the goal is to correct transmissions with at most a single error. For a transmitted message of length n there are 12 LECTURE 6. COPING WITH BIT ERRORS Figure 6-5: A code word in systematic form for a block code. Any linear code can be transformed into an equivalent systematic code. n + 1 situations the receiver has to distinguish between: no errors and a single error in any of the n received bits. Then, depending on the detected situation, the receiver can make, if necessary, the appropriate correction. Our first observation, which we will state here without proof, is that any linear code can be transformed into a systematic code. A systematic co...
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This document was uploaded on 02/26/2014 for the course CS 6.02 at MIT.

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