有限域上一类高次方程的解OA
SOLUTIONS FOR A HIGHER-DEGREE EQUATION OVER FINITE FIELDS
设m是正整数,F23m是含有23m个元素的有限域.本文研究了有限域F23m上的如下方程x22m+ax2m+bx=0,其中a,b∈ F*23m.利用Bluher论文有关定理及线性化多项式、置换多项式的相关结论,本文确定了方程解的个数,并刻画了方程有相应解数时系数a,b所要满足的条件.所得结果在序列的相关性研究、编码的构造研究及密码函数的差分性质研究中有潜在的应用.
Let m be a positive integer and F23m the finite field with 23m elements.We investigates the following equation over the finite field F23m x22m+ax2m+bx=0,where a,b ∈F*23m.By applying relevant theorems from Bluher's work and properties of linearized polynomials and permutation polynomials,we determine the number of solutions to the above equation and characterize the conditions on a and b for each possible solution count.The result may have potential applications in the study of the correlation properties of certain sequences,code constructions,and differential properties of cryptographic functions.
钟可欣;夏永波
中南民族大学数学与统计学学院,湖北武汉 430074中南民族大学数学与统计学学院,湖北武汉 430074
数理科学
有限域线性化多项式置换多项式高次方程
Finite fieldlinearized polynomialpermutation polynomialequation of higher degree
《数学杂志》 2026 (3)
134-140,7
国家自然科学基金资助项目(62171479)中南民族大学中央高校基本科研业务费专项资金项目(CZZ25008).
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