FAN Jinmei, ZHANG Yanhai. Optimal Quinary Cyclic Codes with Minimum Distance Four[J]. Chinese Journal of Electronics, 2020, 29(3): 515-524. doi: 10.1049/cje.2020.02.011
Citation: FAN Jinmei, ZHANG Yanhai. Optimal Quinary Cyclic Codes with Minimum Distance Four[J]. Chinese Journal of Electronics, 2020, 29(3): 515-524. doi: 10.1049/cje.2020.02.011

Optimal Quinary Cyclic Codes with Minimum Distance Four

doi: 10.1049/cje.2020.02.011
Funds:  This work is supported by Scientific Research Project of Education Department of Guangxi (No.2017KY0241) and Natural Science Foundation of Guangxi (No.2018GXNSFBA281019).
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  • Corresponding author: ZHANG Yanhai (corresponding author) was born in Shandong Province, China, in 1977. He received the M.E degree in Faculty of Physics and Electronic Technology from Hubei University. His research interests include communication theory and techniques and mobile communication. (Email:zhang.yanhai@foxmail.com)
  • Received Date: 2018-06-27
  • Rev Recd Date: 2018-09-18
  • Publish Date: 2020-05-10
  • The necessary and sufficient condition for the quinary cyclic codes with generator polynomial (x + 1)mα(x)mαe (x) to have parameters [5m-1; 5m-2m-2; 4] is provided by analyzing solutions of certain equations over the finite field F5m. And thus several classes of new optimal quinary cyclic codes with the same parameters and generator polynomial are constructed based on analyzing irreducible factors of certain polynomials with low degrees over finite fields.
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