Communications Toolbox

gflineq

Find a particular solution of Ax = b over a prime Galois field

Syntax

• x = gflineq(A,b,p);
  [x,vld] = gflineq(A,b,p);
  

Description

Note    This function performs computations in GF(p) where p is odd. To work in GF(2m), apply the \ or / operator to Galois arrays. For details, see Solving Linear Equations.

x = gflineq(A,b,p) returns a particular solution of the linear equation A x = b over GF(p), where p is a prime number. If A is a k-by-n matrix and b is a vector of length k, then x is a vector of length n. Each entry of A, x, and b is an integer between 0 and p-1. If no solution exists, then x is empty.

[x,vld] = gflineq(...) returns a flag vld that indicates the existence of a solution. If vld = 1, then the solution x exists and is valid; if vld = 0, then no solution exists.

Examples

The code below produces some valid solutions of a linear equation over GF(3).

• A = [2 0 1;
       1 1 0;
       1 1 2];
  % An example in which the solutions are valid
  [x,vld] = gflineq(A,[1;0;0],3)
  
  x =
  
       2
       1
       0
  
  
  vld =
  
       1
  

By contrast, the command below finds that the linear equation has no solutions.

• [x2,vld2] = gflineq(zeros(3,3),[2;0;0],3)
  This linear equation has no solution.
  
  x2 =
  
       []
  
  
  vld2 =
  
       0
  

Algorithm

gflineq uses Gaussian elimination.

See Also
gfadd, gfdiv, gfroots, gfrank, gfconv, conv

gffilter

gfminpol