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# Binary repetition code

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6. Let be the binary repetition code with parameter [n, k] = [12, 4].
a) Give a generator matrix for that is in standard form. What does standard form means?
b) Give a parity check matrix for that is in standard form.
c) What is the minimum distance of ?
d) What is the minimum distance of ?
e) What is the dimension of ?
f) What is the dimension of ?
g) How many codewords are in ? List them.
h) How many codewords are in ? List them

#### Solution Preview

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6. Let be the binary repetition code with parameter [n, k] = [12, 4].
a) Give a generator matrix for that is in standard form. What does standard form means?
b) Give a parity check matrix for that is in standard form.
c) What is the minimum distance of ?
d) What is the minimum distance of ?
e) What is the dimension of ?
f) What is the dimension of ?
g) How many codewords are in ? List them.
h) How many codewords are in ? List them

Solution 59

Let £ be the binary repetition code => n = 12, k = 4, m = n - k = 12 - 4 = 8

a) Standard form means the form in which the generator matrix can be expressed as

G = [ Ik P ]

Where Ik is an identity matrix of order ( k x k) and P is a order ( k x m)

 Generator matrix is standard form is given by

G = [ 1 ...

#### Solution Summary

This provides several questions about binary repetition code including generator and parity check matrices, distance, dimension, and codewords.

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