Question

How to perform division of polynomials over gf(2)

Answer 1

Answer:

Step-by-step explanation:

First of all, GF(2) is a sweet little finite field. Recall that the

number 2 is the first prime. [For a number to be prime, it must have exactly

two distinct divisors, 1 and itself.]

• GF(2) consists of the set {0, 1}. The two elements of this set

obey the following addition and multiplication rules:

0 + 0 = 0 0 X 0 = 0

0 + 1 = 1 0 X 1 = 0

1 + 0 = 1 1 X 0 = 0

1 + 1 = 0 1 X 1 = 1

0 - 0 = 0

1 - 0 = 1

0 - 1 = 0 + 1 = 1

1 - 1 = 1 + 1 = 0

• So the addition over GF(2) is equivalent to the logical XOR

operation, and multiplication to the logical AND operation.

• Examples of polynomials defined over GF(2):

x3 + x2 − 1

−x5 + x4 − x2 + 1

x + 1

Hope it helps you....