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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.