Minimal linear codes have interesting applications in secret sharing schemes and secure two-party computation. This paper uses characteristic functions of some subsets of $\mathbb{F}_q$ to construct minimal linear codes. By properties of characteristic functions, we can obtain more minimal binary linear codes from known minimal binary linear codes, which generalizes results of Ding et al. [IEEE Trans. Inf. Theory, vol. 64, no. 10, pp. 6536-6545, 2018]. By characteristic functions corresponding to some subspaces of $\mathbb{F}_q$, we obtain many minimal linear codes, which generalizes results of [IEEE Trans. Inf. Theory, vol. 64, no. 10, pp. 6536-6545, 2018] and [IEEE Trans. Inf. Theory, DOI: 10.1109/TIT.2019.2918537]. Finally, we use characteristic functions to present a characterization of minimal linear codes from the defining set method.
翻译:最小线性代码在秘密共享计划和安全双方计算中具有有趣的应用。 本文使用某些子集的特性函数$mathbb{F ⁇ q$来构建最小线性代码。 通过特性函数的特性,我们可以从已知的最小二进制线性代码中获取更多最起码的二进制线性代码,该二进制代码将Ding等人的结果概括化 [IEEE Trans. Inf. Theory, vol. 64, No. 10, pp. 6536- 6545, 2018] 。 通过相当于$\mathbb{F ⁇ q$的某些子空间的特性功能, 我们获得了许多最起码的线性代码, 它将[IEE. Transy. Inf., vol. 64, no. 6536- 6545, pp. 201818] 和 [IEEEEE. Transer. Inf. Thery, DI: 10.109/TIT.2019.29 18537] 。 最后, 我们使用特性功能从定义的设定方法中描述最低线性代码的特征。