The hull of a linear code plays an important role in determining the complexity of algorithms for checking permutation equivalence of two linear codes and computing the automorphism group of a linear code. Regarding the quantum error correction, linear codes with determined hull are used to construct quantum codes. In this paper, we focus on the hull of Simplex codes and punctured Simplex codes. We firstly study the properties of the matrix produced by the column vectors of a projective space and determine the Euclidean and Hermitian hull of punctured Simplex codes completely. Secondly, we investigate the Euclidean and Hermitian hull of several classes of linear codes from Simplex codes.

线性码的外壳对于确定检查两个线性码的置换等价性和计算线性码的自同构群的算法的复杂度起着重要作用。对于量子纠错，使用具有确定外壳的线性码来构造量子码。在本文中，我们重点关注单纯形码的外壳和穿孔单纯形码。我们首先研究了射影空间的列向量产生的矩阵的性质，并完全确定了穿孔单纯形码的欧几里德和埃尔米特包。其次，我们研究了来自单纯形码的几类线性码的欧几里得和埃尔米特外壳。