# Find the error patterns for the syndrome being 0 0 0.

The full problem is

Consider a (5,2) linear block code C with generator matrix:

G = [1 0 1 1 0; 0 1 0 1 1]

1. Determine the parity check matrix H of C;

2. How many error patterns of C;

3. How many errors can the code correct?

4. Construct the following table;

5. Use the table above to find the most likely codeword v, given that the noisy received codeword is r = (1 1 1 1 0)

6. List all error patterns for the syndrome being 0 0 0.

Note that the problems #1-5 were solved by the student.

The student asked to check if the answers for #1-5 are correct and provide a solution for #6.

See the attached file for the problem.

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#### Solution Preview

#1-4: correct

#5: Another way of solving it. Find the s = r.H^T = 011 which gives error pattern = 01000. ...

#### Solution Summary

This posting helps find the error patterns in a code. In this solution, error patterns which gives all-zero syndrome are determined and explained. It also helps determine the parity check matrix, error patterns, errors that can be corrected by the code, helps construct a table and use it to find a codeword.