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02/18/05 5:49pm

How do you create a recursive Matrix form like the Hadamard Matrix (Used for generating the Walsh Function) in mathematica?

Walsh Function :

W[0] = {0}
W[4] = {{0,0},{0,1}}
W[2n] = {{W[n],W[n]},{W[n], ~W[n]}}

where ~W[n] is the complement of W[n] i.e. where W[n] is 0, ~W[n] is a 1 and vice versa.

W[8] = {{W[4],W[4]},{W[4], ~W[4]}}
~W[4] = {{1,1},{1,0}}

Also, how do you design a Linear Feedback Shift Register in Mathematica? I want to implement a basic PN Sequence and demonstrate its properties like maximum lenght and co.

for an arbitrary prime polynomial in the GF2N field.

example x^7 + x^2 + 1, where addition is modulo 2 is the PN sequence and this is used to create an m-sequence. How do I do this in mathematica?

An helpfull hint will be appreciated.



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