GF(3^4)



Hi everybody,

hope all is well with you.

I am working on a (2,n)-Threshold Secret Sharing Scheme based on the vector space construction. My example works over the elements of GF(2)^4. I am not sure about the right setting of my parameters for any random number of participants.

Can anybody tell me the elements of GF(3)^4 expressed as polynomials?

V = GF(2)^4 ; 16 elements

expressed as polynomials:

V = {0, 1, X, X+1, X^2, X^2+1, X^2+X, X^2+X+1, X^3, X^3+1, X^3+X, X^3+X+1,
X^3 + X^2, X^3 + X^2 + 1, X^3 + X^2 + X, X^3 + X^2 + X + 1}

T = GF(3)^4 ; 81 elements
expressed as polynomials:
?

Thanks you.

Regards,
 Sara