galois.bch_valid_codes

galois.bch_valid_codes(n: int, t_min: int = 1) → List[Tuple[int, int, int]]

Returns a list of $(n, k, t)$ tuples of valid primitive binary BCH codes.

A BCH code with parameters $(n, k, t)$ is represented as a $[n, k, d]_{2}$ linear block code with $d = 2 t + 1$ .

Parameters¶

n: int¶: The codeword size $n$ , must be $n = 2^{m} - 1$ .
t_min: int = 1¶: The minimum error-correcting capability. The default is 1.

Returns¶

A list of $(n, k, t)$ tuples of valid primitive BCH codes.

See also

BCH

References¶

https://link.springer.com/content/pdf/bbm%3A978-1-4899-2174-1%2F1.pdf

Examples¶

In [1]: galois.bch_valid_codes(31)
Out[1]: [(31, 26, 1), (31, 21, 2), (31, 16, 3), (31, 11, 5), (31, 6, 7), (31, 1, 15)]

In [2]: galois.bch_valid_codes(31, t_min=3)
Out[2]: [(31, 16, 3), (31, 11, 5), (31, 6, 7), (31, 1, 15)]