Galois Rings

Magma provides facilities for computing with Galois rings. The features are currently very basic, but advanced features will be available in the near future, including support for the creation of subrings and appropriate embeddings, allowing lattices of compatible embeddings, just as for finite fields.

Because of the valuation defined on them, Galois rings are Euclidean rings, so they may be used in Magma in any place where general Euclidean rings are valid. This includes many matrix and module functions, and the computation of Gröbner bases. Linear codes over Galois rings will also be supported in the near future.

Features:

• Creation of a default Galois ring (using a default defining polynomial).
• Creation of a Galois ring by a specified defining polynomial.
• Basic structural operations and arithmetic.
• Euclidean operations.