See addition and multiplication tables.

Binary values expressed as polynomials in GF(2^m) can readily be manipulated using the definition of this finite field. Addition operations take place as bitwise XOR on m-bit coefficients. Multiplication is defined modulo P(x), where P(x) is a primitive polynomial of degree m. This online tool serves as a polynomial calculator in GF(2^m).

Select input polynomials as decimal coefficients separated by spaces and a P(x) defining GF(2^m).

Model C-182 GALOIS FIELD CALCULATOR A: B: A + B A - B A × B A / B P(x): 11 : P[x] = x+1 111 : P[x] = x2+x+1 1011 : P[x] = x3+x+1 1101 : P[x] = x3+x2+1 10011 : P[x] = x4+x+1 11001 : P[x] = x4+x3+1 100101 : P[x] = x5+x2+1 101001 : P[x] = x5+x3+1 101111 : P[x] = x5+x3+x2+x+1 110111 : P[x] = x5+x4+x2+x+1 111011 : P[x] = x5+x4+x3+x+1 111101 : P[x] = x5+x4+x3+x2+1 1000011 : P[x] = x6+x+1 1011011 : P[x] = x6+x4+x3+x+1 1100001 : P[x] = x6+x5+1 1100111 : P[x] = x6+x5+x2+x+1 1101101 : P[x] = x6+x5+x3+x2+1 1110011 : P[x] = x6+x5+x4+x+1 Discussion  Polynomials  MATLAB

Multiplication in GF(8), based on P(x) = x³ + x + 1

Tue May 21 19:58:24 ADT 2013 Last Updated: 17 FEB 2013	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...