Three-weight cyclic codes and their weight distributions

—Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms, compared with linear block codes. In this paper, seven classes of three-weight cyclic codes over GF(p) whose duals have two zeros are presented, where p is an odd prime. The weight distributions of the seven classes of cyclic codes are settled. Some of the cyclic codes are optimal in the sense that they meet certain bounds on linear codes. The application of these cyclic codes in secret sharing is also considered.

• Type: Journal
• Year: 2016
• Where: DM
• Authors: Cunsheng Ding, Chunlei Li, Nian Li, Zhengchun Zhou
• Keywords: DM 2016