This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English version of the page.

Note: This page has been translated by MathWorks. Click here to see
To view all translated materials including this page, select Country from the country navigator on the bottom of this page.


Find particular solution of Ax = b over prime Galois field


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



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

x = gflineq(A,b) outputs a particular solution of the linear equation A x = b in GF(2). The elements in a, b and x are either 0 or 1. If the equation has no solution, 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, 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, x is empty.

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


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)

The output is below.

x =


vld =


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

[x2,vld2] = gflineq(zeros(3,3),[2;0;0],3)

The output is below.

This linear equation has no solution.

x2 =


vld2 =



gflineq uses Gaussian elimination.

See Also

| | | | |

Introduced before R2006a