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# BaseField -- the field of a code

- Usage:
    `C.BaseField`
- Inputs:
  - C, an instance of the type LinearCode,
- Outputs:
  - a Galois field,

## Description

Given a linear code C over a Galois field $F$, this symbol is used as a key for storing the Galois field $F$.

This symbol is provided by the package CodingTheory.

    i1 : C = linearCode(GF(8,Variable => b), {{1,0,b,0,0},{0,b,b+1,1,0},{1,1,1,b,0}})

                                           5
    o1 = LinearCode{AmbientModule => (GF 8)                                              }
                    BaseField => GF 8
                    cache => CacheTable{}
                    Code => image | 1 0   1 |
                                  | 0 b   1 |
                                  | b b+1 1 |
                                  | 0 1   b |
                                  | 0 0   0 |
                    GeneratorMatrix => | 1 0 b   0 0 |
                                       | 0 b b+1 1 0 |
                                       | 1 1 1   b 0 |
                    Generators => {{1, 0, b, 0, 0}, {0, b, b + 1, 1, 0}, {1, 1, 1, b, 0}}
                    ParityCheckMatrix => | 1 b2+1 b2+1 b2+1 0 |
                                         | 0 0    0    0    1 |
                                             2       2       2
                    ParityCheckRows => {{1, b  + 1, b  + 1, b  + 1, 0}, {0, 0, 0, 0, 1}}

    o1 : LinearCode

    i2 : C.BaseField

    o2 = GF 8

    o2 : GaloisField

## For the programmer

The object BaseField is a symbol.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/CodingTheory.m2:2868:0.