Mince the garlic. Chop the tarragon. Scrub the clams, discarding any that have opened. Place clams and wine in a large pot; cook, covered, over medium-high heat, shaking occasionally, until all the clams have opened, about 6 minutes.
Remove pot from heat and allow clams to cool. Remove clams from shells; if using steamers, pull off the black portion of the neck. Swish clams in the cooking liquid to remove any loose sand. Strain cooking liquid through cheesecloth or a coffee filter. Chop clams and put them in a bowl with the strained cooking liquid. Add 1 tablespoon of the olive oil. Heat the remaining 3 tablespoons of the olive oil over low heat in a small saucepan. Add the garlic and cook until soft, about 3 minutes. Add the tarragon and red-pepper flakes and cook for 2 minutes more. Add the clams and cooking liquid, bring to a simmer, and remove saucepan from the heat. Season with salt and pepper.
NOTE: Recipe can be made to this point several hours ahead.
Cook the pasta in boiling, salted water until tender. Meanwhile, reheat the clam sauce if made ahead. Drain the pasta and return to the pot. Toss linguine with the clam sauce and adjust the seasoning, if desired. Serve immediately.
Makes 4 servings.
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