关于交换预半群的合痕与强合痕
On isotopisms and strong isotopisms of commutative presemifields
摘要：
本文证明了Bierbrauer在\cite{BierbrauerSub}中构造的$P(q,\ell)$（$q$奇素幂和$\ell>1$奇）交换半域与Budaghyan和Helleseth在\cite{BuHe2008}中构造的某些交换预半群是同位素的.证明了它们是强同位素的当且仅当$q\equiv 1(mod\,4)$。因此，对于每个$q\equiv -1(mod\,4)$，存在定义CCZ-不等平面DO多项式的$q^{2\ell}$（$\ell>1$奇）阶的同位素交换预半群.
英文摘要：
In this paper we prove that the $P(q,\ell)$ ($q$ odd prime power and $\ell>1$ odd) commutative semifields constructed by Bierbrauer in \cite{BierbrauerSub} are isotopic to some commutative presemifields constructed by Budaghyan and Helleseth in \cite{BuHe2008}. Also, we show that they are strongly isotopic if and only if $q\equiv 1(mod\,4)$. Consequently, for each $q\equiv -1(mod\,4)$ there exist isotopic commutative presemifields of order $q^{2\ell}$ ($\ell>1$ odd) defining CCZ--inequivalent planar DO polynomials.
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。
