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 |
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.