Balanced gray codes

[sameer]

There are methods to produce balanced gray codes: gray codes where the transitions of each bit are evenly distributed across the mapping.

Wikipedia entry describes it better in more concrete mathematical terms.

One algorithm I thought of:

• Generate a gray code hypercube -- a graph where each vertex is a binary code, and it is connected to all vertices which are 1 bit different (i.e. for bit width of 4, there are 4 adjacent vertices to 0: 1, 2, 4, 8)
• Find hamiltonian cycles in the graph
• Check hamiltonian cycles for balance, pick the first balanced one

I read some papers about it, but I don't have an algorithm that would be simple enough to implement in SystemVerilog.

• http://emis.impa.br/EMIS/journals/EJC/Volume_3/PDF/v3i1r25.pdf
• Hamiltonian Cycles on a hypercube
• Counting sequences
• Canonical form of gray codes in n-cubes
• Balancing cyclic R-ary Gray Codes
• Convert a perfect matching into a Hamiltonian cycle

[Butterwell]

See: https://electronics.stackexchange.com/questions/446249/circuit-balanced-gray-code-binary