In this paper, we give a generalization on the error correcting capability of twisted centralizer codes obtained from a fixed rank 1 matrix. In particular, we fix the combinatorial matrix which is obtained by getting the linear combination of the matrix whose all entries are 1 and the identity matrix of order n. Results reveal that such codes have a dimension 1 for any fixed combinatorial matrix and constant a hence having a relatively low information rate due to the way its codewords are constructed, but are found to be maximum distance separable codes.

翻译：本文对由固定秩-1矩阵导出的扭曲中心化子码的纠错能力进行了推广研究。具体而言，我们固定组合矩阵，该矩阵由所有元素均为1的矩阵与n阶单位矩阵的线性组合得到。结果表明，对于任意固定的组合矩阵与常数a，此类码的维数为1，由于其码字构造方式导致信息率相对较低，但被发现是极大距离可分码。