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hello and welcome to this lecture series on finite field for the control coding my name is Damita Marcia Bay and today we are going to discuss about binary field okay but before we discuss binary field lets quickly review some of the concept that we have learned or basically the definition of the field okay a field is basically a triplet set together the two operation addition and multiplications if and only if it is satisfying certain conditions and the very first of those condition is that multiplication has to be distributive over addition what that means is that for all ABC element of s a times B plus C should be equal to a times B plus a times C apart from this condition this set F under multiplication should be a commutative group so it must satisfy closure associative law identity inverse as well as commutativity now non zero element of this set F under multiplication should also form a commutative group so it should satisfy nonzero element of the set F so to satisfy closure a