## Journal of Applied Mathematics

### The Weight Distributions of a Class of Cyclic Codes with Three Nonzeros over 𝔽3

#### Abstract

Cyclic codes have efficient encoding and decoding algorithms. The decoding error probability and 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 of cyclic 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 exponential sums 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 application of 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.

#### Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 686138, 11 pages.

Dates
First available in Project Euclid: 2 March 2015

https://projecteuclid.org/euclid.jam/1425305887

Digital Object Identifier
doi:10.1155/2014/686138

Mathematical Reviews number (MathSciNet)
MR3232927

#### Citation

Liu, Xiaogang; Luo, Yuan. The Weight Distributions of a Class of Cyclic Codes with Three Nonzeros over 𝔽 3. J. Appl. Math. 2014 (2014), Article ID 686138, 11 pages. doi:10.1155/2014/686138. https://projecteuclid.org/euclid.jam/1425305887

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