Converse, under the Nike brand umbrella since 2003, is suing 31 companies, alleging that those companies are selling sneakers modeled on its iconic Chuck Taylor design in violation of Converse trademarks.

Among the companies named by Converse in the suit, filed Tuesday in the Eastern District of New York and at the International Trade Commission, are Wal-Mart Stores Inc. WMT, -1.02% and Ed Hardy, a unit of Iconix Brand Group Inc. ICON, +2.44% . According to an Associated Press report, Converse says the companies are infringing trademarks that cover the look of the canvas shoe and the diamond pattern on the sole.