Communications Toolbox

gflineq

Solve the linear equation Ax = b over a prime Galois field

Syntax

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

Description

x = gflineq(A,b) returns a particular solution of the linear equation A x = b over GF(2). 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 either 0 or 1. If no solution exists, then x is empty.

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.

[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(2).

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

x =

     1
     1
     0


vld =

     1

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

[x2,vld2] = gflineq(zeros(3,3),[1;0;0])
This linear equation has no solution.

x2 =

     []


vld2 =

     0

Algorithm

gflineq uses Gaussian elimination.

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

gffilter

gfminpol