Without getting into the complexity of pitch diameters of gears, here's an approximation that will get you in the ball park.
L = distance bolt must retract to allow gate to be opened
N = desired number of revolutions of wheel needed to retract bolt
Then the circumference of the gear attached to the wheel, C, must be approximately
C = L / N
and the diameter of the gear, D, must be
D = C/pi
Rack and pinion assemblies are commercially available but they are likely to be expensive. Think about making your own.
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