Low Complexity Normal Elements over Finite Fields of Characteristic Two

@article{Masuda2008LowCN,
  title={Low Complexity Normal Elements over Finite Fields of Characteristic Two},
  author={Ariane M. Masuda and Lucia Moura and Daniel Panario and David Thomson},
  journal={IEEE Transactions on Computers},
  year={2008},
  volume={57},
  pages={990-1001}
}
In this paper, we extend previously known results on the complexities of normal elements. Using algorithms that exhaustively test field elements, we are able to provide the distribution of the complexity of normal elements for binary fields with degree extensions up to 39. We also provide current results on the smallest known complexity for the remaining degree extensions up to 512 by using a combination of constructive theorems and known exact values. We give an algorithm to exhaustively… CONTINUE READING

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