Problem 53950. Time reverse indices

Richard Allred

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Time reverse the index values as follows
IndexIn = [7 1 0]    
IndexOut = [7 6 0]
Note that the indices are zero based and sorted from largest to smallest.
You can think of this as a time reversal of a vector:
[7 1 0] --> [1     1     0     0     0     0     0     1 ] 
[7 6 0] --> [1     0     0     0     0     0     1     1 ]
Here is a second example
[8 4 3 2 0]  --> [ 1     0     1     1     1     0     0     0     1 ]
[8 6 5 4 0]  --> [ 1     0     0     0     1     1     1     0     1 ]
Background of problem.  The index defines the tap positions (or characteristic polynomial) of a Linear Feedback Shift Register (LFSR).  When the polynomial is primitive, the LFSR goes through all possible states before repeating, thus creating a psuedo random binary sequence (PRBS). A curious property is that if the tap positions are reversed, as we are doing in this problem, then the output sequence is also reversed.