Sep 18, 2017

# (WALSH CODES) WALSH CODES ARE GENERATED FROM HADAMARD MATRICES CONSISTING OF 0’S AND 1’S….

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(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

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.

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