Main Content

Find particular solution of `Ax`

= `b`

over
prime Galois field

`x = gflineq(A,b)`

x = gflineq(A,b,p)

[x,vld] = gflineq(...)

**Note**

This function performs computations in GF(p), where p is prime.
To work in GF(2^{m}), 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 = 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)

The output is below.

This linear equation has no solution. x2 = [] vld2 = 0

`gflineq`

uses Gaussian elimination.