Number of gray codes on a constellation
I wonder how many binary gray codes exists for a constellation?
A constellation is a set of points in 2D-space, and as mentioned in http://en.wikipedia.org/wiki/Constellation_diagram, there is a corresponding gray code (http://en.wikipedia.org/wiki/Gray_code).
At the time, I am only interested in circular and square constellation of size $2^k$ points for an arbitrary $k$.
My first guess was $nlog(n)!$, since there is a permutation possible and where the zero is, was proven wrong by exhaustive counting of circular constellation of size 8 (PSK8), which have 96 gray codes.
If anyone can prove it or give a counter example on the square for this formula, it would be very good.
combinatorics
edited Nov 28 '18 at 14:38
amWhy
192k28225439
asked Feb 18 '14 at 15:33
mnzmnz
795
add a comment |
I wonder how many binary gray codes exists for a constellation?
A constellation is a set of points in 2D-space, and as mentioned in http://en.wikipedia.org/wiki/Constellation_diagram, there is a corresponding gray code (http://en.wikipedia.org/wiki/Gray_code).
At the time, I am only interested in circular and square constellation of size $2^k$ points for an arbitrary $k$.
My first guess was $nlog(n)!$, since there is a permutation possible and where the zero is, was proven wrong by exhaustive counting of circular constellation of size 8 (PSK8), which have 96 gray codes.
If anyone can prove it or give a counter example on the square for this formula, it would be very good.
combinatorics
edited Nov 28 '18 at 14:38
amWhy
192k28225439
asked Feb 18 '14 at 15:33
mnzmnz
795
add a comment |
I wonder how many binary gray codes exists for a constellation?
A constellation is a set of points in 2D-space, and as mentioned in http://en.wikipedia.org/wiki/Constellation_diagram, there is a corresponding gray code (http://en.wikipedia.org/wiki/Gray_code).
At the time, I am only interested in circular and square constellation of size $2^k$ points for an arbitrary $k$.
My first guess was $nlog(n)!$, since there is a permutation possible and where the zero is, was proven wrong by exhaustive counting of circular constellation of size 8 (PSK8), which have 96 gray codes.
If anyone can prove it or give a counter example on the square for this formula, it would be very good.
combinatorics
edited Nov 28 '18 at 14:38
amWhy
192k28225439
asked Feb 18 '14 at 15:33
mnzmnz
795
I wonder how many binary gray codes exists for a constellation?
A constellation is a set of points in 2D-space, and as mentioned in http://en.wikipedia.org/wiki/Constellation_diagram, there is a corresponding gray code (http://en.wikipedia.org/wiki/Gray_code).
At the time, I am only interested in circular and square constellation of size $2^k$ points for an arbitrary $k$.
My first guess was $nlog(n)!$, since there is a permutation possible and where the zero is, was proven wrong by exhaustive counting of circular constellation of size 8 (PSK8), which have 96 gray codes.
If anyone can prove it or give a counter example on the square for this formula, it would be very good.
combinatorics
combinatorics
edited Nov 28 '18 at 14:38
amWhy
192k28225439
asked Feb 18 '14 at 15:33
mnzmnz
795
edited Nov 28 '18 at 14:38
amWhy
192k28225439
asked Feb 18 '14 at 15:33
mnzmnz
795
edited Nov 28 '18 at 14:38
amWhy
192k28225439
edited Nov 28 '18 at 14:38
amWhy
192k28225439
edited Nov 28 '18 at 14:38
amWhy
192k28225439
192k28225439
asked Feb 18 '14 at 15:33
mnzmnz
795
asked Feb 18 '14 at 15:33
mnzmnz
795
asked Feb 18 '14 at 15:33
mnzmnz
795
795
add a comment |
add a comment |
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