2013/03/03 by Xiaogang Liu, Yuan Luo, Liu, Xiaogang +1
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Computer and information sciences #Finite Group Theory Research #Information Theory (cs.IT) #cs.IT #graph theory and CDMA systems #math.IT
paper · pdf · doi:10.48550/arxiv.1303.0503
10 pages, 3 tables
openalex publication_date 2013/03/03 · arxiv created 2013/09/01 · arxiv updated 2013/09/03 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
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 form and exponential sum but limited to low moments. In this paper, we focus on the application of higher moments of the exponential sum to determine the weight distributions of a class of ternary cyclic codes with three nonzeros, combining with not only quadratic form 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.