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.
Cooks' note: Toast seeds in a dry heavy skillet over moderate heat, stirring until fragrant and a shade or two darker. Or, toast in a shallow baking pan in a 350°F oven, 5 to 10 minutes.