Centraliser codes

作者：Alahmadi Adel; Alamoudi Shefa; Karadeniz Suat; Yildiz Bahattin; Praeger Cheryl; Sole Patrick^*

来源：Linear Algebra and Its Applications, 2014, 463: 68-77.

DOI：10.1016/j.laa.2014.08.024

• Group centralisers
• Matrix codes
• Cyclic matrices
• Separable matrices

Centraliser codes are codes of length n(2) defined as centralisers of a given matrix A of order n. Their dimension, parity-check matrices, syndromes, and automorphism groups are investigated. A lower bound on the dimension is n, the order of A. This bound is met when the minimal polynomial is equal to the annihilator, i.e. for so-called cyclic (a.k.a. non-derogatory) matrices. If, furthermore, the matrix is separable and the adjacency matrix of a graph, the automorphism group of that graph is shown to be abelian and to be even trivial if the alphabet field is of even characteristic.

• 出版日期2014-12-15
• 单位TELECOM ParisTech