I am sorry this is happening to your Koi. The growths you are seeing might be a viral infection called Carp Pox. This is a version of a herpes virus. The following website will give you some basic information.
The following website gives information on Carp Pox along with some pictures of what it can look like.
Next is another site that gives information on treatment/management, with more pictures.
One final site give a little more information.
It is also possible that this could be an atypical presentation of something else, a bacterial or fungal infection. If you haven't already done so, you may want to test the pond water to make sure everything is as it should be. Before attempting to treat with any medications (as in the case of a bacterial or fungal or even a parasitic infection) I would at least want to know that water chemistry is where it needs to be. I would also want an expert in Koi to visually inspect the pond and the Koi to protect your investment.
I hope this helps, and that your Koi are ok. Please let me know if I can be of further assistance. Best of luck with your pond.
I am afraid your diagnosis is incorrect. None of the pictures in the websites you sent resemble anything close to the problem on my goldfish. These are not koi; I have various species of goldfish. It seems, based on my further and continuing research, that other fish can sometimes quite possibly develop carp pox or other such diseases, but, as I said, nothing in these websites resembles the problem I identified. The search for continues. Thank you, anyway.