Combine sugar, water, soda, and salt in a large Dutch oven; cook over medium heat, stirring constantly, until sugar dissolves. Cover and continue to cook over medium heat 2 to 3 minutes to wash down sugar crystals from sides of pan. Uncover and cook, without stirring, until mixture reaches soft ball stage (234°).
Gradually add whipping cream, without stirring. Continue cooking over medium heat until mixture reaches hard ball stage (260°).
Remove from heat; pour mixture into a well-buttered 15- x 10- x 1-inch jellyroll pan. Allow mixture to cool slightly.
Work mixture into a mound, using a buttered spatula or candy scraper. Pick up mound with buttered hands; pull, fold, and twist until candy is opaque and begins to stiffen. Divide candy in half, and pull each half into a rope, 1/2-inch in diameter. Twist ropes together, and cut into 1-inch pieces. Wrap each piece in waxed paper.