| 摘要: |
| 本文研究了有限域上只有零解的n元n次方程的结构问题.利用对有限域上不可约多元多项式在其扩域中的分解特征的刻画，结合Chevalley定理，得到了有限域上n元n次方程只有零解的一个充要条件，并给出这类方程的一些新的具体构造. |
| 关键词: 有限域 方程只有零解 多元多项式分解 不可约多项式 |
| DOI： |
| 分类号:O153.4 |
| 基金项目:国家自然科学基金资助（61272484）；信息保障科学技术实验室开放基金资助（KJ-12-02）. |
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| THE STRUCTURE OF THE EQUATION OVER FLNITE FLELDS WITH n UNKNOWNS AND WITH DEGREE n WHICH VANISH ONLY AT ZERO |
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CHEN Xi1, QU Long-jiang1, LI Chao1,2
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1.Departement of Mathematics and System Science, National University of Defense Technology, Changsha 410073, China;2.Information Assurance Science and Technology Laboratory, Beijing 100072, China
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| Abstract: |
| In this paper, we investigate the structure of the equation over finite fields with n unknowns and with degree n which vanish only at zero. By using the factorization of the irreducible multivariable polynomial in some extension field and with the Chevalley Theorem, a su-cient and necessary condition of the equation with n unknowns and with degree n which vanish only at zero is obtained. Furthermore, we construct some explicit equations of this class. |
| Key words: finite field equation which vanish only at zero multivariate polynomial factorization irreducible polynomial |
