Put the carrots in a sieve set over a bowl. Toss carrots with 1 tablespoon of the salt and let stand to get rid of excess water, about 45 minutes. Gently press carrots against the sieve to remove any remaining moisture. Rinse and drain. Place the carrots in a clean kitchen towel, then twist the towel to squeeze out any excess water. Repeat the process using the daikon. Whisk together the sugar and vinegar until sugar is completely dissolved. Divide this pickling mixture among 3 quart-size plastic bags, and set 1 bag aside to use in Step 4. Add the carrots and daikon separately to the other 2 bags, seal and toss to coat evenly. Lay bags flat on a plate and refrigerate at least 24 hours, turning the bags over every hour if possible. After about 20 hours, repeat step 1 using the cucumbers. After draining, place the cucumbers in the third plastic bag of pickling mix, seal, and toss to coat. Lay the bag flat on a plate and refrigerate for 4 to 6 hours, turning bag every hour if possible. The cucumber needs only 4 to 6 hours to absorb the flavor of the vinegar marinade. Drain the carrots, daikon and cucumbers well at room temperature for 30 to 45 minutes before serving.;
Recipe courtesy of Corinne Trang from "Authentic Vietnamese Cooking: Food from a Family Table" Simon & Schuster, 1999.