Galois Fields 1 Fields Designtheory Form

Instructions and help about Galois Fields 1 Fields Designtheory

so remember a field with a finite number of elements is called the galwa field and so the question you've got to ask yourself is self what does a galwa field look like so remember the key properties for a field plus and times are commutative there's an additive identity which we call zero there's a multiplicative identity which we call one every element has an additive inverse every non-zero element has a multiplicative inverse for a b and c in our field a times b plus c is a v plus ac and there's a few useful propositions one the identity uniqueness the additive and multiplicative identities in a field are unique and there's product in some uniqueness if b is not equal to c then a plus b is not equal to a plus c and as long as a is not our additive identity a times b is not equal to a times c so let's find the addition and multiplication tables for a field of two elements since a field needs to contain an additive identity zero and a multiplicative identity one then our field needs to