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Binary linear block code

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June 18th, 2023

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 .

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