The Weight Distributions of Cyclic Codes and Elliptic Curves
Baocheng Wang, Chunming Tang, Yanfeng Qi, Yixian Yang, Maozhi Xu · IEEE Transactions on Information Theory · 2012
Cyclic codes with two zeros and their dual codes as a practically and theoretically interesting class of linear codes have been studied for many years and find many applications. The determination of the weight distributions of such codes is an open problem. Generally, the weight distributions of cyclic codes are difficult to determine. Utilizing a class of elliptic curves, this paper determines the weight distributions of dual codes ofq-ary cyclic codes with two zeros for a few more cases, whereqis an odd prime power.