A note on linearized polynomials and the dimension of their kernels

作者：Ling, San; Qu, Longjiang^*

来源：Finite Fields and Their Applications, 2012, 18(1): 56-62.

DOI：10.1016/j.ffa.2011.06.002

• Linearized polynomials
• Kernel
• Finite field

Recently explicit representations of the class of linearized permutation polynomials and the number of such polynomials were given in Zhou (2008) [4] and Yuan and Zeng (2011) [3]. In this paper, we generalize this result to linearized polynomials with kernel of any given dimension, solving an open problem in Charpin and Kyureghyan (2009) [1]. Moreover, more explicit representations of such polynomials are given and several classes of explicit linearized polynomials with kernel of any given dimension are presented.

• 出版日期2012-1
• 单位中国人民解放军国防科学技术大学; 南阳理工学院