In this paper we consider in detail the composition of an irreducible polynomial with X2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X^2$$\end{document} and suggest a recurrent construction of irreducible polynomials of fixed degree over finite fields of odd characteristics. More precisely, given an irreducible polynomial of degree n and order 2rt\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^rt$$\end{document} with t odd, the construction produces ordt(2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ord_t(2)$$\end{document} irreducible polynomials of degree n and order t. The construction can be used for example to search irreducible polynomials with specific requirements on its coefficients.

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有限域上固定次数的不可约多项式的递归构造

在本文中，我们详细考虑了不可约多项式与 X2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage 的组合{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$X^2$$\end{document} 并建议在有限域上循环构造固定次数的不可约多项式奇怪的特征。更准确地说，给定 n 阶不可约多项式和阶 2rt\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs } \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^rt$$\end{document} 与 t 奇数，构造产生 ordt(2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ord_t(2)$$\end{document} n 阶和 t 阶不可约多项式。例如，该构造可用于搜索对其系数有特定要求的不可约多项式。