Cut the corn away from the cob. Place the kernels in the bottom of a colander over the sink.
Bring a large pot of salted water to a boil. Add the pasta and cook 2-3 minutes, or according to the directions on the package. Reserve 1 cup of cooking water, then drain the pasta over the corn. Return to the empty pan.
Add the avocado, dill, and 1/2 cup of cooking water to a blender. Blend until smooth, thinning with additional water if needed. Season to taste with salt and pepper. Pour the avocado sauce over the pasta. Add the crab and mix well to ensure the pasta is evenly coated with sauce.