ウォルシュ変換

最近ウォルシュ変換と行列を考えています。以下の問題を解こうとしています。
１How is the Walsh matrix or Hadamard matrix constructed from the Walsh functions.
2. What is the purpose of two separate matrices, sequence ordered and natural ordered?
3. Is a "Gray permutation", which converts the natural order to the sequence order, simply rearranging the columns from 0,1,2,3,4 order to 0,1,3,2,6... order?