hw13 - 1 4. Suppose the code f above is modifed to a code g...

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MAT 312/AMS 351 – Fall 2010 Homework 12b 1. Is this a group code? Explain your answer. 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 0 0 1 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 . 2. f : 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 1 0 1 1 1 1 0 1 0 0 1 1 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 0 0 0 and g : 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 1 0 1 1 0 1 1 1 1 0 0 1 0 0 1 1 0 1 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 1 1 0 0 0 1 are both group codes. Calculate the minimum distance d between code- words for f and for g . Is g better than f for error-detection? Is g better than f for error-correction? 3. In the previous exercise, f can be used to detect up to 2 errors in the transmission of a word, or to correct 1 error in the transmission of a word, but not both. Explain carefully why.
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Unformatted text preview: 1 4. Suppose the code f above is modifed to a code g by using two copies oF the third check bit: g : 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 1 0 1 1 0 1 1 1 1 0 0 1 0 0 1 1 0 0 1 0 1 1 0 1 1 1 1 0 0 1 1 1 1 1 1 0 0 0 0 . Is g a group code? Is g any better than f For error-detection and correction? Explain. 5. Write out explicitly (as above) the code f : B 4 B 7 with generator matrix: 1 0 0 0 1 0 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 0 0 0 1 0 0 0 . What is d For this code? How could you make it more useFul For error control without increasing code-word length? 2...
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hw13 - 1 4. Suppose the code f above is modifed to a code g...

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