与多线性多项式乘积有关的方程的解的个数
The number of solutions of an equation related to a product of multilinear polynomials
摘要：
我们来看看一个方程的解的个数，形式为f_1*f_2*. * f_k=a，其中f_i是一个多线性多项式.对于a=0，a<>0的情形，我们用两种方法构造了该问题的解，一般得到一个半显式公式。我们表明，该公式可以生成比传统算法更有效的算法，传统算法需要进行系统的计算。在某些特殊情况下，我们也给出了显式公式，并将我们的主要结果应用于分离变量多重线性码的权族的搜索。
英文摘要：
We look at the number of solutions of an equation of the form f_1*f_2*...*f_k=a in a finite field, where each f_i is a multilinear polynomial. We use two methods to construct a solution of this problem for the cases a=0, a<>0, and we generally get a semi-explicit formula. We show that this formula can generate a more efficient algorithm than the traditional algorithm which consists to make a systematic computation. We also give explicit formulas in some special cases, and an application of our main result to the search of the weight hierarchy of the multilinear code with separated variables.
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。
