The Weight Distributions of a Class of Cyclic Codes with Three Nonzeros over𝔽3 | Zendy

Xiaogang Liu | Zendy; Yuan Luo | Zendy

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The Weight Distributions of a Class of Cyclic Codes with Three Nonzeros over𝔽₃

Author(s) -

Xiaogang Liu,

Yuan Luo

Publication year - 2014

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2014/686138

Subject(s) - quadratic equation , exponential function , mathematics , focus (optics) , class (philosophy) , ternary operation , weight distribution , bounded function , discrete mathematics , computer science , mathematical analysis , physics , geometry , engineering , artificial intelligence , optics , programming language , aerospace engineering

Cyclic codes have efficient encoding and decoding algorithms. The decoding error probabilityand the undetected error probability are usually bounded by or given from the weight distributions of the codes. Most researches are about the determination of the weight distributions ofcyclic codes with few nonzeros, by using quadratic forms and exponential sums but limited to low moments. In this paper, we focus on the application of higher moments of the exponentialsums to determine the weight distributions of a class of ternary cyclic codes with three nonzeros, combining with not only quadratic forms but also MacWilliams’ identities. Another applicationof this paper is to emphasize the computer algebra system Magma for the investigation of the higher moments. In the end, the result is verified by one example using Matlab

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