秩为2的半域的一个合数问题的解
Solution to an isotopism question concerning rank 2 semifields
摘要：
在美国，Dempwolff：Dembowski-Ostrom多项式的更多平移平面和半域，设计，代码，加密。\textbf{68}（1-3）（2013），81-103]，作者给出了三类秩为2的阶为$q^{2n}$的半域的构造，其中$q$和$n$是奇数，使用Dembowski-Ostrom多项式。这些半域是否是新的问题，即与以前的构造不是同位素的问题，是一个悬而未决的问题。在本文中，我们解决了这个问题的$n>3$，特别是我们证明了这些类中的两个，标记为$D_{A}$和$D_{AB}$，是新的$n>3$，而presemifields家庭$D_{B}$是同位素的广义扭曲字段的每个$n\geq 3$。
英文摘要：
In [U. Dempwolff: More Translation Planes and Semifields from Dembowski-Ostrom Polynomials, Designs, Codes, Cryptogr. \textbf{68} (1-3) (2013), 81-103], the author gives a construction of three classes of rank two semifields of order $q^{2n}$, with $q$ and $n$ odd, using Dembowski-Ostrom polynomials. The question whether these semifields are new, i.e. not isotopic to previous constructions, is left as an open problem. In this paper we solve this problem for $n>3$, in particular we prove that two of these classes, labeled $D_{A}$ and $D_{AB}$, are new for $n>3$, whereas presemifields in family $D_{B}$ are isotopic to Generalized Twisted Fields for each $n\geq 3$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
