Some Properties of Binary Gray Code

The binary Gray code, or the reflected binary code, is a code whose code-word changes only one bit and the Hamming distance of two adjacent code-words is always one. Although the binary Gray code itself has many plications and is related to theoretical or practical facts, we are interested in it as a transforming function from a residue numbers modulo a power of 2 to a product of binary number of certain size. In this paper, we especially focus on the weight of n-the code-word, and give some properties of the weight which might help us to lead a map with a required characteristics.