See addition and multiplication tables.

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 10000011 : P[x] = x7+x+1 10001001 : P[x] = x7+x3+1 10001111 : P[x] = x7+x3+x2+x+1 10010001 : P[x] = x7+x4+1 10011101 : P[x] = x7+x4+x3+x2+1 10100111 : P[x] = x7+x5+x2+x+1 10101011 : P[x] = x7+x5+x3+x+1 10111001 : P[x] = x7+x5+x4+x3+1 10111111 : P[x] = x7+x5+x4+x3+x2+x+1 11000001 : P[x] = x7+x6+1 11001011 : P[x] = x7+x6+x3+x+1 11010011 : P[x] = x7+x6+x4+x+1 11010101 : P[x] = x7+x6+x4+x2+1 11100101 : P[x] = x7+x6+x5+x2+1 11101111 : P[x] = x7+x6+x5+x3+x2+x+1 11110001 : P[x] = x7+x6+x5+x4+1 11110111 : P[x] = x7+x6+x5+x4+x2+x+1 11111101 : P[x] = x7+x6+x5+x4+x3+x2+1 100011011 : P[x] = x8+x4+x3+x+1 100011101 : P[x] = x8+x4+x3+x2+1 100101011 : P[x] = x8+x5+x3+x+1 100101101 : P[x] = x8+x5+x3+x2+1 101001101 : P[x] = x8+x6+x3+x2+1 101011111 : P[x] = x8+x6+x4+x3+x2+x+1 101100011 : P[x] = x8+x6+x5+x+1 101100101 : P[x] = x8+x6+x5+x2+1 101101001 : P[x] = x8+x6+x5+x3+1 101110001 : P[x] = x8+x6+x5+x4+1 110000111 : P[x] = x8+x7+x2+x+1 110001101 : P[x] = x8+x7+x3+x2+1 110101001 : P[x] = x8+x7+x5+x3+1 111000011 : P[x] = x8+x7+x6+x+1 111001111 : P[x] = x8+x7+x6+x3+x2+x+1 111100111 : P[x] = x8+x7+x6+x5+x2+x+1 111110101 : P[x] = x8+x7+x6+x5+x4+x2+1

Discussion Polynomials MATLAB

Multiplication in GF(8), based on P(x) = x^{3} + x + 1