universeCode -- linear code $\mathtt{F}^\mathtt{n}$

Synopsis

Usage:

universeCode(F,n)
Inputs:
- F, a Galois field,
- n, an integer,
Outputs:
- an instance of the type LinearCode,

Description

Returns the code with largest dimension such that its length is n and the entries of its codewords are in the field F.

i1 : F = GF(2,3);

i2 : n=7;

i3 : C=universeCode(F,n)

                                  7
o3 = LinearCode{AmbientModule => F                                                                                                                                                             }
                BaseField => F
                cache => CacheTable{}
                GeneratorMatrix => | 1 0 0 0 0 0 0 |
                                   | 0 1 0 0 0 0 0 |
                                   | 0 0 1 0 0 0 0 |
                                   | 0 0 0 1 0 0 0 |
                                   | 0 0 0 0 1 0 0 |
                                   | 0 0 0 0 0 1 0 |
                                   | 0 0 0 0 0 0 1 |
                Generators => {{1, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 1}}
                ParityCheckMatrix => 0
                ParityCheckRows => {{}}

o3 : LinearCode

i4 : C.ParityCheckMatrix

o4 = 0

              1       7
o4 : Matrix ZZ  <-- ZZ

Ways to use universeCode :

universeCode(GaloisField,ZZ)

For the programmer

The object universeCode is a method function.