数学杂志2026，Vol.46Issue(3)：134-140,7.
有限域上一类高次方程的解
SOLUTIONS FOR A HIGHER-DEGREE EQUATION OVER FINITE FIELDS
摘要
Abstract
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.关键词
有限域/线性化多项式/置换多项式/高次方程Key words
Finite field/linearized polynomial/permutation polynomial/equation of higher degree分类
数理科学引用本文复制引用
钟可欣,夏永波..有限域上一类高次方程的解[J].数学杂志,2026,46(3):134-140,7.基金项目
国家自然科学基金资助项目(62171479) （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). （CZZ25008）
