As a subclass of linear codes, cyclic codes have important applications in consumer electronics, data storage systems and communication systems. In this paper, a new family of optimal ternary cyclic codes with minimum distance five are obtained from known perfect nonlinear functions over \(\mathbb {F}_{3^{m}}\). Moreover, we investigate the weight distributions of their duals.

中文翻译：

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具有最小距离为 5 的最优三进制循环码族及其对偶

作为线性码的一个子类，循环码在消费电子、数据存储系统和通信系统中有着重要的应用。在本文中，从\(\mathbb {F}_{3^{m}}\) 上的已知完美非线性函数中获得了具有最小距离为5 的一组新的最优三元循环码。此外，我们研究了它们对偶的权重分布。