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The Weight Distributions of Cyclic Codes and Elliptic Curves

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5 Author(s)
Baocheng Wang ; Coll. of Inf. Eng., North China Univ. of Technol., Beijing, China ; Chunming Tang ; Yanfeng Qi ; Yixian Yang
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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 of q-ary cyclic codes with two zeros for a few more cases, where q is an odd prime power.

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Information Theory, IEEE Transactions on  (Volume:58 ,  Issue: 12 )