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Binary linear block code

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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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Solution Summary

This provides an example of answering several questions regarding binary linear block code, including generator and parity check matrices, distance, errors, and codewords.

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Please see the attached file.

-----54

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 .

Solution 54

[n,k] =[6,3]

n=6, k=3
Therefore m= n-k = 3

a) G = [ 1 0 1 1 0 1
0 1 1 0 0 1
0 0 1 1 1 0 ]
c1 c2 c3 c4 c5 c6

Performing c3 => c3 - c6

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

Now a matrix in standard form is a one in which the generator matrix takes ...

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