AmbientModule -- the ambient module of a code

Synopsis

Usage:

C.AmbientModule
Inputs:
- C, an instance of the type LinearCode,
Outputs:
- a module,

Description

Given a linear code C of length $n$ over a Galois Field $F$, this symbol is used as a key for storing the free module $F^n$, which is referred to as the ambient module of C.

This symbol is provided by the package CodingTheory.

i1 : C = linearCode(GF(4,Variable => a), {{1,0,a,0,0},{0,a,a+1,1,0},{1,1,1,a,0}})

                                       5
o1 = LinearCode{AmbientModule => (GF 4)                                              }
                BaseField => GF 4
                cache => CacheTable{}
                Code => image | 1 0   1 |
                              | 0 a   1 |
                              | a a+1 1 |
                              | 0 1   a |
                              | 0 0   0 |
                GeneratorMatrix => | 1 0 a   0 0 |
                                   | 0 a a+1 1 0 |
                                   | 1 1 1   a 0 |
                Generators => {{1, 0, a, 0, 0}, {0, a, a + 1, 1, 0}, {1, 1, 1, a, 0}}
                ParityCheckMatrix => | 1 a+1 a+1 a+1 0 |
                                     | 0 0   0   0   1 |
                ParityCheckRows => {{1, a + 1, a + 1, a + 1, 0}, {0, 0, 0, 0, 1}}

o1 : LinearCode

i2 : C.AmbientModule

           5
o2 = (GF 4)

o2 : GF 4-module, free

For the programmer

The object AmbientModule is a symbol.