Optimal Quinary Cyclic Codes with Minimum Distance Four

FAN Jinmei; ZHANG Yanhai

doi:10.1049/cje.2020.02.011

Volume 29 Issue 3

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FAN Jinmei and ZHANG Yanhai, “Optimal Quinary Cyclic Codes with Minimum Distance Four,” Chinese Journal of Electronics, vol. 29, no. 3, pp. 515-524, 2020, doi: 10.1049/cje.2020.02.011

Citation:

FAN Jinmei and ZHANG Yanhai, “Optimal Quinary Cyclic Codes with Minimum Distance Four,” Chinese Journal of Electronics, vol. 29, no. 3, pp. 515-524, 2020, doi: 10.1049/cje.2020.02.011

FAN Jinmei and ZHANG Yanhai, “Optimal Quinary Cyclic Codes with Minimum Distance Four,” Chinese Journal of Electronics, vol. 29, no. 3, pp. 515-524, 2020, doi: 10.1049/cje.2020.02.011

Citation:

FAN Jinmei and ZHANG Yanhai, “Optimal Quinary Cyclic Codes with Minimum Distance Four,” Chinese Journal of Electronics, vol. 29, no. 3, pp. 515-524, 2020, doi: 10.1049/cje.2020.02.011

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Optimal Quinary Cyclic Codes with Minimum Distance Four

doi: 10.1049/cje.2020.02.011

College of Science, Guilin University of Technology, Guilin 541004, China

Funds: This work is supported by Scientific Research Project of Education Department of Guangxi (No.2017KY0241) and Natural Science Foundation of Guangxi (No.2018GXNSFBA281019).

More Information

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

Abstract

Abstract

The necessary and sufficient condition for the quinary cyclic codes with generator polynomial (x + 1)m_α(x)m_αe (x) to have parameters [5^m-1; 5^m-2^m-2; 4] is provided by analyzing solutions of certain equations over the finite field F^5m. 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.
- Finite field,
- Cyclic code,
- Irreducible polynomial,
- Monomial

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References(20)

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