Minimal linear codes have important applications in secret sharing schemes and secure multi-party computation, etc. In this paper, we study the minimality of a kind of linear codes over $\mathrm{GF}(p)$ from Maiorana-McFarland functions. We first obtain a new sufficient condition for this kind of linear codes to be minimal without analyzing the weights of its codewords, which is a generalization of some works given by Ding et al. in 2015. Using this condition, it is easy to verify that such minimal linear codes satisfy $\frac{w_{\min }}{w_{\max }}\le \frac{p-1}{p}$ for any prime p, where $w_{\min }$ and $w_{\max }$ denote the minimum and maximum nonzero weights in a code, respectively. Then, by selecting the subsets of $\mathrm{GF}{(p)}^s$, we present two new infinite families of minimal linear codes with $\frac{w_{\min }}{w_{\max }}\le \frac{p-1}{p}$ for any prime p. In addition, the weight distributions of the presented linear codes are determined in terms of Krawtchouk polynomials or partial spreads.

最小线性码在秘密共享方案和安全的多方计算等方面具有重要的应用。在本文中，我们研究了一种线性码在 $\mathrm{GF}（p）$来自Maiorana-McFarland的功能。我们首先获得一种新的充分条件，使这种线性代码在不分析其代码字权重的情况下达到最小，这是Ding等人给出的一些工作的概括。在2015年。使用此条件，很容易验证此类最小线性代码是否满足$\frac{w_{\mathrm{分}}}{w_{\mathrm{最高}}}\le \frac{p-\mathrm{1个}}{p}$对于任何素数p，其中$w_{\mathrm{分}}$ 和 $w_{\mathrm{最高}}$分别表示代码中的最小和最大非零权重。然后，通过选择$\mathrm{GF}{（p）}^s$，我们提出了两个新的最小线性代码的无限系列 $\frac{w_{\mathrm{分}}}{w_{\mathrm{最高}}}\le \frac{p-\mathrm{1个}}{p}$对于任何素数p。此外，根据Krawtchouk多项式或部分扩展来确定给出的线性代码的权重分布。