ring(LinearCode) -- the ring of a code

Function: ring
Usage:

ring LinearCode
Inputs:
- C, an instance of the type LinearCode,
Outputs:
- a ring,

Description

Given a code C, returns the ring that contains the entries of the generator matrix of C.

i1 : C = hammingCode(2, 3)

                                       7
o1 = LinearCode{AmbientModule => (GF 2)                                                                                   }
                BaseField => GF 2
                cache => CacheTable{}
                Code => image | 1 1 0 1 |
                              | 1 1 1 0 |
                              | 1 0 1 1 |
                              | 1 0 0 0 |
                              | 0 1 0 0 |
                              | 0 0 1 0 |
                              | 0 0 0 1 |
                GeneratorMatrix => | 1 1 1 1 0 0 0 |
                                   | 1 1 0 0 1 0 0 |
                                   | 0 1 1 0 0 1 0 |
                                   | 1 0 1 0 0 0 1 |
                Generators => {{1, 1, 1, 1, 0, 0, 0}, {1, 1, 0, 0, 1, 0, 0}, {0, 1, 1, 0, 0, 1, 0}, {1, 0, 1, 0, 0, 0, 1}}
                ParityCheckMatrix => | 1 1 1 1 0 0 0 |
                                     | 0 1 0 1 1 1 0 |
                                     | 1 0 0 1 1 0 1 |
                ParityCheckRows => {{1, 1, 1, 1, 0, 0, 0}, {0, 1, 0, 1, 1, 1, 0}, {1, 0, 0, 1, 1, 0, 1}}

o1 : LinearCode

i2 : ring(C)

o2 = GF 2

o2 : GaloisField

Ways to use this method:

ring(LinearCode) -- the ring of a code

The source of this document is in /__w/M2/M2/macaulay2-1.26.05+ds/M2/Macaulay2/packages/CodingTheory.m2:3514:0.