A note on linearized polynomials and the dimension of their kernels - Ling, San (2013)
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.