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    Generating a code that detects errors

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    Construct a (7,3) code that detects 3 errors and do the following...
    a) Write the generator matrix
    b) Show by example that your code will detect 1 error, 2 errors, and 3 errors.
    c) Give an example where 4 errors are made in transmitting a message word, but your code does not detect any errors.
    d) How many errors are corrected by your code?
    e) Give an example where your code detects errors in a received word, but cannot correct the errors.

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    Solution Preview

    ** Please see the attached file for the complete solution **
    (a) We wish to find a generator matrix for a (7,3) code that detects up to 3 errors.

    The following generator matrix will accomplish this:
    (please see the attached file)

    (b) We wish to show by ...

    Solution Summary

    In this solution we generate a (7,3) code capable of detecting up to 3 errors and investigate some of its properties.