The Weight Distributions of Cyclic Codes and Elliptic Curves
Baocheng Wang, Chunming Tang, Yanfeng Qi, Yixian Yang, Maozhi Xu
TL;DR
This paper investigates the weight distributions of dual cyclic codes with two zeros by leveraging properties of elliptic curves, advancing understanding of their structure and potential applications.
Contribution
It introduces new methods to determine weight distributions of dual cyclic codes with two zeros using elliptic curve techniques, extending previous results.
Findings
Derived weight distributions for specific dual cyclic codes with two zeros
Connected elliptic curve properties to coding theory problems
Enhanced methods for analyzing cyclic code weight distributions
Abstract
Cyclic codes with two zeros and their dual codes as a practically and theoretically interesting class of linear codes, have been studied for many years. However, the weight distributions of cyclic codes are difficult to determine. From elliptic curves, this paper determines the weight distributions of dual codes of cyclic codes with two zeros for a few more cases.
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Taxonomy
TopicsCoding theory and cryptography · Islamic Finance and Communication · Educational Curriculum and Learning Methods