| it is fin rot. Usually, that is a result of sub-par water quality. Please tell us something about your filter system, and how oftern you clean them.
I cannot tell from the photo what the white spots are. Can you try to put the koi in a bowl and take a photo from the top ?
while you at at it, please try this :
rotten fin : clean it with Iodine (H2O2 will be OK), apply triple anti biotic ointment
white spot : clean it with hydrogen per-oxide. apply same triple -anti bitotic ointment if you like. This white spot could be fungus florish on opening created by parasites. H2O2 will take care of the fungus.
stan |