Constructions of irreducible polynomials over finite fields with even characteristic

被引：0

作者：

P. L. Sharma

Shalini Ashima

Mansi Gupta

Sushil Harish

机构：

[1] HP University,Department of Mathematics & Statistics

来源：

Indian Journal of Pure and Applied Mathematics | 2023年 / 54卷

关键词：

Finite field; Irreducible polynomial; Reciprocal polynomial; Trace function; Composition of polynomials; 12E05; 12E10; 12E20;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

For a finite field Fq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {F}_q$$\end{document}, where q=2s,s∈N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q=2^s, s \in \mathbb {N}$$\end{document}, we present some results regarding the constructions of irreducible polynomials of degree 4n over Fq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {F}_q$$\end{document} by using the method of composition of polynomials from a given irreducible polynomial p(x) having degree n≥1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n \ge 1$$\end{document} over Fq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {F}_q$$\end{document}.

引用

页码：734 / 742

页数：8

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