komm.RepetitionCode

Repetition code. For a given length $n \geq 1$, it is the linear block code whose only two codewords are $00 \cdots 0$ and $11 \cdots 1$. The repetition code has the following parameters:

• Length: $n$
• Dimension: $k = 1$
• Redundancy: $m = n - 1$
• Minimum distance: $d = n$

For more details, see LC04, Sec. 3.7 and EC Zoo: Repetition code.

Notes

• Its dual is the single parity-check code.

Parameters:

• n (int) –

  The length $n$ of the code. Must be a positive integer.

Examples:

>>> code = komm.RepetitionCode(5)
>>> (code.length, code.dimension, code.redundancy)
(5, 1, 4)
>>> code.generator_matrix
array([[1, 1, 1, 1, 1]])
>>> code.check_matrix
array([[1, 1, 0, 0, 0],
       [1, 0, 1, 0, 0],
       [1, 0, 0, 1, 0],
       [1, 0, 0, 0, 1]])
>>> code.minimum_distance()
5

>>> code = komm.RepetitionCode(16)
>>> code.codeword_weight_distribution()
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
>>> code.coset_leader_weight_distribution()
[1, 16, 120, 560, 1820, 4368, 8008, 11440, 6435, 0, 0, 0, 0, 0, 0, 0, 0]