Stir together soy sauce, vinegar, oil, red pepper flakes, garlic, and ginger.
Cook linguine in a large pot of boiling salted water until just tender, then drain in a colander and rinse under cold water until cool. Toss with dressing, carrot, scallions, sesame seeds, and radishes in a large bowl.
** It is rare, but some people with nut allergies have sensitivity to sesame as well. Be sure to ask before serving.