It has been proved in Bierbrauer and Kyureghyan (Des. Codes Cryptogr. 46:269–301, 2008) that a binomial function aX i + bX j can be crooked only if both exponents i, j have 2-weight ≤2. In the present paper we give a brief construction for all known examples of crooked binomial functions. These consist of an infinite family and one sporadic example. The construction of the sporadic example uses the properties of an algebraic curve of genus 3. Computer experiments support the conjecture that each crooked binomial is equivalent either to a member of the family or to the sporadic example.
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机译：在Bierbrauer和Kyureghyan（Des。Codes Cryptogr。46：269–301，2008）中已证明，只有在以下情况下，二项式函数aX i + bX j 才能被歪曲。两个指数i，j的2权重≤2。在本文中，我们简要介绍了扭曲二项式函数的所有已知示例。这些包括一个无限的家庭和一个零星的例子。零星示例的构造使用了属3的代数曲线的特性。计算机实验支持这样的猜想，即每个弯曲的二项式都等同于家庭成员或零星示例。
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