Walsh codes:-
Walsh codes are generated from Hadamard matrices consisting of 0's and 1's. Hadamard matrices of order 2k can be found by a simple recursion. Given a Hadamard matrix Hk of order 2k, the matrix Hk+1 is formed as
![](https://book.transtutors.com/qimg/8e0a974f-c030-4916-8f3f-5e8ec1b30adb.png)
Where
k denotes the matrix complementary to Hk, with 1's and 0's interchanged.
(a) Starting with H0 = [0], find H1, H2, and H3.
(b) A Hadamard matrix defines a set of codes from the rows of the matrix. One way is to convert 0's to -1's and use ordinary multiplication. Show that the codes resulting from H1, H2, and H3 each define orthogonal sets.
(c) Argue that orthogonality applies to codes derived from any Hadamard matrix.