galois.GF_factory

galois.GF_factory(characteristic, degree, 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

  • characteristic (int) – The prime characteristic \(p\) of the field \(\mathrm{GF}(p^m)\).

  • degree (int) – The prime characteristic’s degree \(m\) of the field \(\mathrm{GF}(p^m)\).

  • 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 class that is a sublcass of galois.GF.

Return type

galois.GF2, galois.GF2m, galois.GFp, galois.GFpm