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Sat Jun 28 12:52:36 CEST 2008

## symmetric 2D LFSR

For a 2D LFSR grid, the problem to solve is rotation
ambiguity. Instead of using an LFSR generator for each direction, use
2 like in the 1D case, but tile them such that the structure is
rotation-symmetric. I.e. for N=3 the 4 LFSR are wrapped as:
X+ Y+ X- Y-
1 2 3 3 6 9 9 8 7 7 4 1
4 5 6 2 5 8 6 5 4 8 5 2
7 8 9 1 4 7 3 2 1 9 6 3
Analogous to before, this gives 5N^2-4D equations and 4N^2 unknowns,
leading to the solvability condition:
N^2 >= 4D
This looks like a nice idea, but using a 6x6 estimator for D=15 gives
underdetermined equations.. Apparently, there is some information lost
in the XOR.
Intuition: do something like this in |R and you might reduce
condition, but it is hard to get to linear dependence. In a finite
space it is a lot easier to end up with linear dependence because
there is less room.

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