shorten -- shortens a code

Synopsis

Usage:

shorten(LinearCode, List)

shorten(LindearCode, ZZ)
Inputs:
- C, an instance of the type LinearCode,
- L, a list,
- i, an integer,
Outputs:
- an instance of the type LinearCode,

Description

Given a code C of length $n$ and a list L (or an integer i), returns a new code obtained from C by selecting only those codewords of C that have zeros in each of the coordinate positions in the list L (or the position i), and then deleting these positions.

The resulting code will have length $n - r$, where $r$ is the number of elements in L (or 1 when the integer i is used).

a code and a list are given

Usage:

shorten(LinearCode, List)
Inputs:
- C, an instance of the type LinearCode,
- L, a list,
Outputs:
- an instance of the type LinearCode,

Given a code C of length $n$ and a list L, returns a new code obtained from C by selecting only those codewords of C that have zeros in each of the coordinate positions in the list L, and then deleting these positions.

The resulting code will have length $n - r$, where $r$ is the number of elements in L.

i1 : F = GF(2);

i2 : codeLen = 10;

i3 : L = {{0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 1, 1, 0, 1, 0,0}, {1, 1, 0, 0, 0, 1, 0, 0, 1, 0}, {1, 0, 0, 1, 0, 0, 0, 1, 1,1}};

i4 : C = linearCode(F,codeLen,L);

i5 : shorten(C, {3,6,8,9});

a linear code and an integer are given

Usage:

shorten(LinearCode, ZZ)
Inputs:
- C, an instance of the type LinearCode,
- i, an integer,
Outputs:
- an instance of the type LinearCode, $C$

Given a code C of length $n$ and a list L, returns a new code obtained from C by selecting only those codewords of C that have zero in the position i), and then deleting this position.

The resulting code will have length $n - 1$.

i6 : F = GF(2);

i7 : codeLen = 10;

i8 : L = {{0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 1, 1, 0, 1, 0,0}, {1, 1, 0, 0, 0, 1, 0, 0, 1, 0}, {1, 0, 0, 1, 0, 0, 0, 1, 1,1}};

i9 : C = linearCode(F,codeLen,L);

i10 : shorten(C, 3)

                                   9
o10 = LinearCode{AmbientModule => F                                                                                                                                                                                                                                    }
                 BaseField => F
                 cache => CacheTable{}
                 Code => image | 0 1 1 1 0 0 1 0 |
                               | 1 1 1 0 0 0 0 1 |
                               | 0 0 1 1 1 0 0 1 |
                               | 0 0 1 1 1 0 0 1 |
                               | 0 1 0 0 1 0 1 1 |
                               | 0 0 0 0 0 0 0 0 |
                               | 0 0 1 1 1 0 0 1 |
                               | 0 1 1 1 0 0 1 0 |
                               | 0 0 0 0 0 0 0 0 |
                 GeneratorMatrix => | 0 1 0 0 0 0 0 0 0 |
                                    | 1 1 0 0 1 0 0 1 0 |
                                    | 1 1 1 1 0 0 1 1 0 |
                                    | 1 0 1 1 0 0 1 1 0 |
                                    | 0 0 1 1 1 0 1 0 0 |
                                    | 0 0 0 0 0 0 0 0 0 |
                                    | 1 0 0 0 1 0 0 1 0 |
                                    | 0 1 1 1 1 0 1 0 0 |
                 Generators => {{0, 1, 0, 0, 0, 0, 0, 0, 0}, {1, 1, 0, 0, 1, 0, 0, 1, 0}, {1, 1, 1, 1, 0, 0, 1, 1, 0}, {1, 0, 1, 1, 0, 0, 1, 1, 0}, {0, 0, 1, 1, 1, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0}, {1, 0, 0, 0, 1, 0, 0, 1, 0}, {0, 1, 1, 1, 1, 0, 1, 0, 0}}
                 ParityCheckMatrix => | 0 0 1 1 0 0 0 0 0 |
                                      | 1 0 1 0 1 0 0 0 0 |
                                      | 0 0 0 0 0 1 0 0 0 |
                                      | 0 0 1 0 0 0 1 0 0 |
                                      | 1 0 0 0 0 0 0 1 0 |
                                      | 0 0 0 0 0 0 0 0 1 |
                 ParityCheckRows => {{0, 0, 1, 1, 0, 0, 0, 0, 0}, {1, 0, 1, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 1, 0, 0}, {1, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1}}

o10 : LinearCode

Ways to use shorten :

shorten(LinearCode,List)
shorten(LinearCode,ZZ)

For the programmer

The object shorten is a method function.