galois.BCH.extension_field

property galois.BCH.extension_field : type[FieldArray]

The Galois field $GF (q^{m})$ that defines the BCH syndrome arithmetic.

Examples

Construct a binary $BCH (15, 7)$ code.

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

In [2]: bch.extension_field
Out[2]: <class 'galois.GF(2^4)'>

In [3]: print(bch.extension_field.properties)
Galois Field:
  name: GF(2^4)
  characteristic: 2
  degree: 4
  order: 16
  irreducible_poly: x^4 + x + 1
  is_primitive_poly: True
  primitive_element: x

Construct a $BCH (26, 14)$ code over $GF (3)$ .

In [4]: bch = galois.BCH(26, 14, field=galois.GF(3)); bch
Out[4]: <BCH Code: [26, 14, 7] over GF(3)>

In [5]: bch.extension_field
Out[5]: <class 'galois.GF(3^3)'>

In [6]: print(bch.extension_field.properties)
Galois Field:
  name: GF(3^3)
  characteristic: 3
  degree: 3
  order: 27
  irreducible_poly: x^3 + 2x + 1
  is_primitive_poly: True
  primitive_element: x