Show that the codes resulting from h1 h2 and h3nbspeach

Question

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 H_k of order 2_k, the matrix H_k+1 is formed as

Where _k denotes the matrix complementary to H_k, 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.