First, let us compare GUAVA's minimum distance
command `MinimumDistance` with an implementation
of Algorithm 1, called `MinDist`.
The first output is the minimum distance, the second is the internal GAP time
it takes for the computation.

gap> Read("/home/wdj/gapfiles/codes/foster_mindist8.gap"); #I Package ``GUAVA'': the C code programs are not compiled. #I Some GUAVA functions, e.g. `ConstantWeightSubcode', will be unavailable. #I See ?Installing GUAVA ---------------------------------------------------------------------------- Loading GUAVA 1.82 (GUAVA Coding Theory Package) by Jasper Cramwinckel, Erik Roijackers, Reinald Baart, Eric Minkes, Lea Ruscio, and David Joyner (http://web.usna.navy.mil/~wdj/homepage.html). ---------------------------------------------------------------------------- gap> C:=RandomLinearCode(20,15,GF(3)); a linear [20,15,1..3]2..5 random linear code over GF(3) gap> MinimumDistance(C);time; 3 9350 gap> MinDist(C);time; 3 10

Next, let us compare an implementation of Algorithm 3, called `MinDistLeon`,
to GUAVA's minimum distance function. The 0 indicates that it finished almost instantly. The 5 elements of
the array are the minimum distances found in each of 5 trials. The second and
third arguments are and , respectively.

gap> Read("/home/wdj/gapfiles/codes/foster_mindist6.gap"); gap> C:=RandomLinearCode(40,20,GF(2)); a linear [40,20,1..7]6..20 random linear code over GF(2) gap> MinimumDistance(C);time; 5 260 gap> MinDistLeon(C,3,3,5);time; [ 5, 5, 5, 5, 6 ] 5 0

**Concluding Remarks**
In the process of writing this code, my advisor and I discovered that GAP had
an error in one of it's kernel functions. In fact, this was a known error that
the developers were not able to track down until we provided them with code
that caused GAP to crash. This enabled the developers to patch the kernel. Not
essential to this project, but a nice benefit.

The essential parts of the project were writing `MinimumDistance`

and
`MinimumDistanceLeon`

. The GAP code for these programs are attached as Appendices.

The improved algorithm presented here is included in version 1.9 of GUAVA (released 4-2004).