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A family of optimal ternary cyclic codes with minimum distance five and their duals
Cryptography and Communications ( IF 1.2 ) Pub Date : 2021-06-01 , DOI: 10.1007/s12095-021-00493-z
Dandan Wang , Xiwang Cao

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:

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。

更新日期:2021-06-02
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