galois.GF

galois.GF(order, prim_poly=None, target='cpu', mode='auto', rebuild=False)[source]

Factory function to construct Galois field array classes of type \(\mathrm{GF}(p^m)\).

Parameters

  • order (int) – The order \(p^m\) of the field \(\mathrm{GF}(p^m)\). Order must be a prime power.

  • prim_poly (galois.Poly, optional) – The primitive polynomial of the field. Default is None which will use the Conway polynomial obtained from galois.conway_poly.

  • target (str) – The target keyword argument from numba.vectorize, either "cpu", "parallel", or "cuda".

  • mode (str, optional) – The type of field computation, either "auto", "lookup", or "calculate". The default is "auto". The “lookup” mode will use Zech log, log, and anti-log lookup tables for speed. The “calculate” mode will not store any lookup tables, but perform field arithmetic on the fly. The “calculate” mode is designed for large fields that cannot store lookup tables in RAM. Generally, “calculate” will be slower than “lookup”. The “auto” mode will determine whether to use “lookup” or “calculate” based on the field size. For “auto”, field’s with order <= 2**16 will use the “lookup” mode.

  • rebuild (bool, optional) – Indicates whether to force a rebuild of the lookup tables. The default is False.

Returns

A new Galois field array class that is a subclass of galois.GFArray.

Return type

type

Examples

Construct various Galois field array classes.

# Construct a GF(2^m) class
In [5]: GF256 = galois.GF(2**8); print(GF256)
<class 'numpy.ndarray' over GF(2^8)>

# Construct a GF(p) class
In [6]: GF571 = galois.GF(571); print(GF571)
<class 'numpy.ndarray' over GF(571)>

# Construct a very large GF(2^m) class
In [7]: GF2m = galois.GF(2**100); print(GF2m)
<class 'numpy.ndarray' over GF(2^100)>

# Construct a very large GF(p) class
In [8]: GFp = galois.GF(36893488147419103183); print(GFp)
<class 'numpy.ndarray' over GF(36893488147419103183)>

See galois.GFArray for more examples of what Galois field arrays can do.