¼teaspoonred chili pepper flakesgochugaru, (finely ground) - optional (see note)
Clean the radish and carrot by scrubbing with a brush and/or scratching off the stubborn impurities with a small knife. Cut into match sticks. You can use a mandoline if you have one. Use the thickest blade.
Add all the remaining ingredients. Mix well by hand until the sugar is dissolved and the radish is evenly coated with the gochugaru (if using). Taste and add more vinegar or sugar to your liking.
Let sit for at least 30 minutes before serving. It will taste better the next day.
If unavailable, you can finely mince the coarse red chili pepper flakes with a knife on a cutting board. You can also mix it with a little bit of warm water to dissolve, and then run it through a strainer before mixing it with radish.