Koi pellets, flakes, or nothing. Really isn't a correct answer for feeding. There is enough algae and what not in your pond to keep your fish happy. The goldfish food will do just fine. I think the only difference is the amount. You get koi food in larger containers than you can get goldfish food.
With my old pond, I went a whole year without feeding my goldfish that I had. There was around 20 that were 5-6". They did just fine. I do however feed my koi that I have not a pellet diet. I don't think there is any real difference for a backyard, as far as brands go. I just get the pellets from wal-mart. Been doing that for years. There are higher prices foods, which will be good for color and growth.
They will really eat just about anything. Cut up fruits and veggies would be a nice treat.
The more you feed, the better filtration system you need. One thing you'll want to keep in mind.
As I stated before, no correct answer.
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