Galois Fields¶

This section contains classes and functions for creating Galois field arrays.

Galois field classes¶

`GF`(order[, irreducible_poly, ...])	Creates a `FieldArray` subclass for \(\mathrm{GF}(p^m)\).
`Field`(order[, irreducible_poly, ...])	Alias of `GF()`.

`FieldArray`(x[, dtype, copy, order, ndmin])	A `ndarray` subclass over \(\mathrm{GF}(p^m)\).

`GF2`(x[, dtype, copy, order, ndmin])	A `ndarray` subclass over \(\mathrm{GF}(2)\).

`primitive_root`(n[, start, stop, method])	Finds a primitive root modulo \(n\) in the range `[start, stop)`.
`primitive_roots`(n[, start, stop, reverse])	Iterates through all primitive roots modulo \(n\) in the range `[start, stop)`.
`is_primitive_root`(g, n)	Determines if \(g\) is a primitive root modulo \(n\).

`irreducible_poly`(order, degree[, method])	Returns a monic irreducible polynomial \(f(x)\) over \(\mathrm{GF}(q)\) with degree \(m\).
`irreducible_polys`(order, degree[, reverse])	Iterates through all monic irreducible polynomials \(f(x)\) over \(\mathrm{GF}(q)\) with degree \(m\).

`primitive_poly`(order, degree[, method])	Returns a monic primitive polynomial \(f(x)\) over \(\mathrm{GF}(q)\) with degree \(m\).
`primitive_polys`(order, degree[, reverse])	Iterates through all monic primitive polynomials \(f(x)\) over \(\mathrm{GF}(q)\) with degree \(m\).
`conway_poly`(characteristic, degree)	Returns the Conway polynomial \(C_{p,m}(x)\) over \(\mathrm{GF}(p)\) with degree \(m\).
`matlab_primitive_poly`(characteristic, degree)	Returns Matlab's default primitive polynomial \(f(x)\) over \(\mathrm{GF}(p)\) with degree \(m\).

`primitive_element`(irreducible_poly[, method])	Finds a primitive element \(g\) of the Galois field \(\mathrm{GF}(q^m)\) with degree-\(m\) irreducible polynomial \(f(x)\) over \(\mathrm{GF}(q)\).
`primitive_elements`(irreducible_poly)	Finds all primitive elements \(g\) of the Galois field \(\mathrm{GF}(q^m)\) with degree-\(m\) irreducible polynomial \(f(x)\) over \(\mathrm{GF}(q)\).
`is_primitive_element`(element, irreducible_poly)	Determines if \(g\) is a primitive element of the Galois field \(\mathrm{GF}(q^m)\) with degree-\(m\) irreducible polynomial \(f(x)\) over \(\mathrm{GF}(q)\).

Last update: May 16, 2022