I need a vector V=[a1,a2,a3,...,a16] such that for every vector X=[x1,x2,x3,...,x16] the product P=V.X=a1.x1+a2.x2+a3.x3+...+a16.x16 is not equal to zero. except zero vector.
where a1,a2,...,a16, x1,x2,...,x16 belongs to Galois field GF(2^8). and both the product and addition coincides with the Galois field GF(2^8).
Any help will be appreciated.