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Find particular solution of Ax = b over a prime Galois field
x = gflineq(A,b,p)
[x,vld] = gflineq(...)
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.
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.
gfadd, gfdiv, gfroots, gfrank, gfconv, conv, Galois Fields of Odd Characteristic
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