Perfect nonlinear binomials and their semifields
Perfect nonlinear binomials and their semifields
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DOI：
10.1016/j.ffa.2008.09.002
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发表时间：
2009-04
期刊：
影响因子：
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通讯作者：
Zhengbang Zha;Gohar M. M. Kyureghyan-Gohar-M.-M.-Kyureghyan-1681417;Xueli Wang
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文献类型：
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作者：
Zhengbang Zha;Gohar M. M. Kyureghyan-Gohar-M.-M.-Kyureghyan-1681417;Xueli Wang
证明了对于适当的整数s和α∈GF（p3k），二项式[公式：见正文]定义了GF（p3k）中的完美非线性映射，它不等价于单项式映射.作为结果，构造了p3k阶交换真半域。在大多数情况下，它们与阿尔伯特的扭曲场不是同位素的，这是p ≥ 5和奇k>1的这种半域的唯一已知例子。
It is proven that for an appropriate choice of an integer s and α∈GF(p3k) the binomial [Formula: see text] defines a perfect nonlinear mapping in GF(p3k), which is not equivalent to a monomial one. As a consequence, commutative proper semifields of order p3kare constructed. In most of the cases those are not isotopic to Albert's twisted fields, which are the only previously known examples of such semifields for p⩾5 and odd k>1.