Title :
The Weight Distributions of Cyclic Codes and Elliptic Curves
Author :
Wang, Baocheng ; Tang, Chunming ; Qi, Yanfeng ; Yang, Yixian ; Xu, Maozhi
Author_Institution :
Coll. of Inf. Eng., North China Univ. of Technol., Beijing, China
Abstract :
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.
Keywords :
cyclic codes; dual codes; linear codes; dual code; elliptic curve; linear code; q-ary cyclic code; weight distribution; zeros; Elliptic curves; Gaussian processes; Hamming weight; Linear code; Polynomials; Cyclic codes; Gaussian periods; elliptic curves; linear codes; weight distribution;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2012.2210386
