I have a list of vectors from a vector space over a finite field of order p for some prime p. For example: I have: {{1,0,1},{0,1,2}} where the vectors are in $\mathbb{F}_3^3$. I want a list of the 9 vectors which are all the linear combinations of my list. For example: from the 2 vectors in the above list I want {{0,0,0},{1,0,1},{2,0,2},{0,2,1},{0,1,2},{1,2,2},{2,1,1},{1,1,0},{2,2,0}}.
$\begingroup$
$\endgroup$
0
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
You could take all possible pairs from your field and use them for linear combinations of your two vectors.
pairs = Flatten[Table[Mod[{i, j}, 3], {i, 0, 2}, {j, 0, 2}], 1];
Mod[pairs . {{1, 0, 1}, {0, 1, 2}} , 3]
answered Sep 9, 2022 at 17:01