Linear codes with good parameters have wide applications in secret sharing schemes, authentication codes, association schemes, consumer electronics and communications, etc. During the past four decades, constructions of linear codes with good parameters received much attention and many classes of such codes were presented. In this paper, we obtain a family of linear codes with good parameters over \(\mathbb {F}_p\) by exploring further properties of constant dimension subspace codes, where p is a prime. The weight distribution of three classes of linear codes presented in this family is determined. Most notably, three classes of linear codes presented in this family are distance-optimal with respect to the Griesmer bound. Also, this paper presents a sufficient and necessary condition for this family of linear codes to have a \(\lambda \)-dimensional hull. In addition, we show that our linear codes can be used to construct secret sharing schemes with interesting access structures and strongly regular graphs.

具有良好参数的线性码在秘密共享方案、认证码、关联方案、消费电子和通信等方面有着广泛的应用。 在过去的 40 年中，具有良好参数的线性码的构建受到了广泛的关注，并提出了许多类别的此类代码. 在本文中，我们通过探索恒维子空间代码的进一步性质，获得了一系列在\(\mathbb {F}_p\) 上具有良好参数的线性代码，其中p是素数。确定了该族中出现的三类线性代码的权重分布。最值得注意的是，该系列中提供的三类线性代码相对于 Griesmer 边界是距离最优的。此外，本文提出了该线性代码族具有\(\lambda \)维外壳的充分必要条件。此外，我们展示了我们的线性代码可用于构建具有有趣访问结构和强正则图的秘密共享方案。