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 $d=2t+1$.

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)]