vectorSpace -- vector space of a code

Synopsis

Usage:

vectorSpace C
Inputs:
- C, an instance of the type LinearCode,
Outputs:
- a module, $V$

Description

Given a linear code C, this function returns $V$, the vector space spanned by the rows of a generator matrix of C.

i1 : H = hammingCode(2,3);

i2 : vectorSpace H

o2 = image | 1 1 1 0 |
           | 1 0 1 1 |
           | 1 1 0 1 |
           | 1 0 0 0 |
           | 0 1 0 0 |
           | 0 0 1 0 |
           | 0 0 0 1 |

                                     7
o2 : GF 2-module, submodule of (GF 2)

The next is an example for the class of EvaluationCode.

i3 : RM = reedMullerCode(2,4,1);

i4 : vectorSpace(RM.LinearCode)

o4 = image | 1 0 0 1 1 |
           | 1 0 0 1 0 |
           | 1 1 1 0 1 |
           | 1 1 1 0 0 |
           | 1 0 0 0 0 |
           | 1 0 0 0 1 |
           | 1 0 1 0 0 |
           | 1 0 1 1 1 |
           | 1 0 1 1 0 |
           | 1 0 1 0 1 |
           | 1 1 0 0 1 |
           | 1 1 0 1 0 |
           | 1 1 0 1 1 |
           | 1 1 0 0 0 |
           | 1 1 1 1 0 |
           | 1 1 1 1 1 |

                                     16
o4 : GF 2-module, submodule of (GF 2)

Ways to use vectorSpace :

vectorSpace(LinearCode)

For the programmer

The object vectorSpace is a method function.