guava - Gap

GUAVA 16
gap> C1:=ElementsCode(m, GF(2));
a (6,8,1..6)2..3 user defined unrestricted code over GF(2)
gap> IsLinearCode(C1);
false
gap> WeightDistribution(C1);
[ 1, 0, 0, 6, 0, 0, 1 ]
In this example we first wrote out a list of strings, then converted them into codewords over
GF(2). The call to ElementsCode constructs a code from a list of elements. It is possible that the set
of codewords we used actually is a vector space, but the call to IsLinearCode says no. Finally the
last function tells us that there are 6 codewords of weight 3, and one each of weights 0 and 6 in this
code.
A very useful feature of GUAVA is the ability to construct random codes:
Example
gap> C:= RandomLinearCode(12,5,GF(2));
a [12,5,?] randomly generated code over GF(2)
An error-correcting code’s properties are fairly well captured by three numbers which traditionally
are referred to using the letters n, k and d. We ask for a random code by specifying n (the wordlength),
and k (the code’s dimension) as well as the field which serves as the alphabet for the code.
One of the most salient features of a code (a feature that determines how good it will be at correcting
errors) is its minimum weight, d. This is the smallest weight of any nonzero word in the code.
If we wish to correct m errors we will need to have a minimum weight of at least 2m + 1.
Example
gap> MinimumWeight(C);
3
This particular code would be capable of correcting single bit errors.
Finally, one might be interested in the entire distribution of the weights of the words in a code.
The weight distribution is a vector that tells us how many words there are in a code with each possible
weight between 0 and n.
Example
gap> WeightDistribution(C);
[ 1, 0, 0, 2, 3, 6, 7, 6, 4, 2, 1, 0, 0 ]