论文标题
在有限场上算术的特征$ 2 $
On finite field arithmetic in characteristic $2$
论文作者
论文摘要
我们有兴趣将$ \ mathbf {f} _ {\！2^n}/\ mathbf {f} _ {\！2} $扩展到$ \ mathbf {f} _ {f} _ {\！2^{nd}}允许的基础的基础的正常基础$ \ mathbf {f} _ {\！2^{nd}} $。汤姆森（Thomson）和韦尔（Weir）最近对这个问题进行了研究，但如果$ d $等于$ 2 $。如果$ d $等于$ 3 $和$ 4 $，我们构建有效的扩展基础。我们还提供了可以将汤姆森 - 韦尔结构与我们的结合结合在一起的条件。
We are interested in extending normal bases of $\mathbf{F}_{\!2^n}/\mathbf{F}_{\!2}$ to bases of $\mathbf{F}_{\!2^{nd}}/\mathbf{F}_{\!2}$ which allow fast arithmetic in $\mathbf{F}_{\!2^{nd}}$. This question has been recently studied by Thomson and Weir in case $d$ is equal to $2$. We construct efficient extended bases in case $d$ is equal to $3$ and $4$. We also give conditions under which Thomson-Weir construction can be combined with ours.
