特征2中的低阶平面单项式
Low-degree planar monomials in characteristic two
摘要：
有限域上的平面函数产生有限射影平面和其他组合对象。它们只存在于奇特征中，但最近周引入了一个偶特征类似物，它具有类似的应用。本文确定了F_q上所有形式为c->uc^t的平面函数，其中q为2的幂，t为整数，0<t<=q^{1/4}，u为F_q的非零元。这解决并深化了施密特和周的一个猜想。
英文摘要：
Planar functions over finite fields give rise to finite projective planes and other combinatorial objects. They exist only in odd characteristic, but recently Zhou introduced an even characteristic analogue which has similar applications. In this paper we determine all planar functions on F_q of the form c-->uc^t, where q is a power of 2, t is an integer with 0<t<=q^{1/4}, and u is a nonzero element of F_q. This settles and sharpens a conjecture of Schmidt and Zhou.
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。
