• Corpus ID: 119663110

Normal elements in finite fields

@article{Hyde2018NormalEI,
  title={Normal elements in finite fields},
  author={Trevor Hyde},
  journal={arXiv: Number Theory},
  year={2018}
}
  • Trevor Hyde
  • Published 6 September 2018
  • Mathematics
  • arXiv: Number Theory
We give a simple derivation of the formula for the number of normal elements in an extension of finite fields. Our proof is based on the fact that units in the Galois group ring of a field extension act simply transitively on normal elements. 
Existence and Cardinality of k-Normal Elements in Finite Fields
TLDR
This paper forms a general lower bound for the number of k-normal elements, assuming that they exist, and derives a new existence condition for k- normal elements using the general factorization of the polynomial $x^m - 1$ into cyclotomic polynomials.

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