Galois field (GF) with R

Question

Is there any package for Galois fields (GF) in R? I would like to define the following matrix operations with GF.

1+1=0
1+0=1
0+1=1
0+0=0

Obviously R doesn't understand the 1+1 without specifying it:

> k <- matrix(c(0,1,1,0,1,0,0,0,0,1), ncol=10);k
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,]    0    1    1    0    1    0    0    0    0     1
> p <- matrix(c(0,0,0,1,1,1,0,1,0,1), ncol=10);p
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,]    0    0    0    1    1    1    0    1    0     1
> c <- k+p;c
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,]    0    1    1    1    2    1    0    1    0     2

Is that the **only** GF you want to use? Or are you looking for advice on implementing an arbitrary field's operators? — Carl Witthoft, Jul 11 '13 at 13:23

score 3 · Accepted Answer · edited May 23 '17 at 12:29

I don't know anything about Galois fields, but from this question it appears that addition and subtraction are equivalent to xor. It might be easier to just use this fact to do your computations.

as.integer(xor(k,p))

Or, if you want to get really fancy, you can overload the operator and define your own class:

`+.GF`<-function (x, y) as.integer((x | y) & !(x & y))
class(k)<-'GF'
class(p)<-'GF'
k+p
[1] 0 1 1 1 0 1 0 1 0 0

score 2 · Answer 2 · answered Jul 11 '13 at 12:37

You could just define a function yourself. It looks like you're just doing boolean arithmetic.

myadd <- function(x, y){(x+y) %% 2}

Example

> a <- matrix(c(0,0,1,1),2,2)
> b <- matrix(c(0,1,0,1),2,2)
> a
     [,1] [,2]
[1,]    0    1
[2,]    0    1
> b
     [,1] [,2]
[1,]    0    0
[2,]    1    1
> myadd(a,b)
     [,1] [,2]
[1,]    0    1
[2,]    1    0

Galois field (GF) with R

2 Answers2