Abstract
Cyclic codes over finite field have been studied for decades due to their wide applications in communication and storage systems. However their weight distributions are known only in a few cases. In this paper, we investigate a class of \begin{document}$ p$\end{document} -ary cyclic codes whose duals have three zeros, where \begin{document}$ p$\end{document} is an odd prime. The weight distributions of the class of cyclic codes for all distinct cases are determined explicitly. The results indicate that these codes contain five-weight codes, seven-weight codes and eleven-weight codes. Some of these codes are optimal. Moreover, the covering structures of the class of codes are considered and being used to construct secret sharing schemes.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
