See attached file for full problem description.
3. Let be a binary linear block code with parameter [n, k] = [6, 3] which has
as its generator matrix. Assume that the first three bits of each codeword are the information bits.
a) Find a generator matrix for that is in standard form. What does standard form means?
b) Find a parity check matrix for that is in standard form.
c) List all the codeword in .
d) What is the minimum distance for ?. Explain.
e) How many errors can correct?. Explain.
f) List the codewords in , the dual code of .
This provides an example of answering several questions regarding binary linear block code, including generator and parity check matrices, distance, errors, and codewords.