关键词: 有限域, 迹函数, 线性化多项式

Abstract: Let C be the companion matrix of a linearized polynomial and I be the identity matrix of the same order. We gave a necessary and sufficient condition for its reversibility by analyzing the structure of C+I, and based on this, we gave linearized polynomials
 whose kernel had trivial intersection with the kernel of trace function.

Key words: finite field, trace function, linearized polynomial