galois.BCH.is_narrow_sense

property galois.BCH.is_narrow_sense : bool

Indicates if the BCH code is narrow-sense, meaning the roots of the generator polynomial are consecutive powers of \(\alpha\) starting at 1, that is \(\alpha, \dots, \alpha^{d-1}\).

Examples¶

Construct a binary narrow-sense \(\textrm{BCH}(15, 7)\) code with first consecutive root \(\alpha\).

In [1]: bch = galois.BCH(15, 7); bch
Out[1]: <BCH Code: [15, 7, 5] over GF(2)>

In [2]: bch.is_narrow_sense
Out[2]: True

In [3]: bch.c == 1
Out[3]: True

In [4]: bch.generator_poly
Out[4]: Poly(x^8 + x^7 + x^6 + x^4 + 1, GF(2))

In [5]: bch.roots
Out[5]: GF([2, 4, 8, 3], order=2^4)

Construct a binary non-narrow-sense \(\textrm{BCH}(15, 7)\) code with first consecutive root \(\alpha^3\). Notice the design distance of this code is only 3.

In [6]: bch = galois.BCH(15, 7, c=3); bch
Out[6]: <BCH Code: [15, 7, 3] over GF(2)>

In [7]: bch.is_narrow_sense
Out[7]: False

In [8]: bch.c == 1
Out[8]: False

In [9]: bch.generator_poly
Out[9]: Poly(x^8 + x^7 + x^6 + x^4 + 1, GF(2))

In [10]: bch.roots
Out[10]: GF([8, 3], order=2^4)