Communications Toolbox

gfrank

Compute the rank of a matrix over a Galois field

Syntax

• rk = gfrank(A,p);
  

Description

Note    This function performs computations in GF(pm) where p is odd. To work in GF(2m), use the rank function with Galois arrays. For details, see Computing Ranks.

rk = gfrank(A,p) calculates the rank of the matrix A in GF(p), where p is a prime number.

Algorithm

gfrank uses an algorithm similar to Gaussian elimination.

Examples

In the code below, gfrank says that the matrix A has less than full rank. This conclusion makes sense because the determinant of A is zero mod p.

• A = [1 0 1;
     2 1 0;
     0 1 1];
  p = 3;
  det_a = det(A); % Ordinary determinant of A
  detmodp = rem(det(A),p); % Determinant mod p
  rankp = gfrank(A,p);
  disp(['Determinant = ',num2str(det_a)])
  disp(['Determinant mod p is ',num2str(detmodp)])
  disp(['Rank over GF(p) is ',num2str(rankp)])
  

The output is below.

• Determinant = 3
  Determinant mod p is 0
  Rank over GF(p) is 2
  

gfprimfd

gfrepcov