A New Criterion on k-Normal Elements over Finite Fields

The notion of normal elements for finite fields extension was generalized as k-normal elements by Huczynska et al. (2013). Several methods to construct k-normal elements were presented by Alizadah et al. (2016) and Huczynska et al. (2013), and the criteria on k-normal elements were given by Alizadah et al. (2016) and Antonio et al. (2018). In the paper by Huczynska, S., Mullen, G., Panario, D. and Thomson, D. (2013), the number of k-normal elements for a fixed finite field extension was calculated and estimated. In this paper the authors present a new criterion on k-normal elements by using idempotents and show some examples. Such criterion was given for usual normal elements before by Zhang et al. (2015).