Journal of Applied Mathematics
- J. Appl. Math.
- Volume 2014 (2014), Article ID 686138, 11 pages.
The Weight Distributions of a Class of Cyclic Codes with Three Nonzeros over 𝔽 3
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.
J. Appl. Math., Volume 2014 (2014), Article ID 686138, 11 pages.
First available in Project Euclid: 2 March 2015
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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