A Note on the Brawley-Carlitz Theorem on Irreducibility of Composed Products of Polynomials over Finite Fields

被引：3

作者：

Munemasa, Akihiro ^{[1
]}

Nakamura, Hiroko ^{[1
]}

机构：

[1] Tohoku Univ, Res Ctr Pure & Appl Math, Grad Sch Informat Sci, Sendai, Miyagi, Japan

来源：

ARITHMETIC OF FINITE FIELDS, WAIFI 2016 | 2016年 / 10064卷

关键词：

Finite field; Composed product; Irreducible polynomial;

D O I：

10.1007/978-3-319-55227-9_7

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We give a new proof of the Brawley-Carlitz theorem on irreducibility of the composed products of irreducible polynomials. Our proof shows that associativity of the binary operation for the composed product is not necessary. We then investigate binary operations defined by polynomial functions, and give a sufficient condition in terms of degrees for the requirement in the Brawley-Carlitz theorem.

引用

页码：84 / 92

页数：9

共 5 条

[1] IRREDUCIBLES AND THE COMPOSED PRODUCT FOR POLYNOMIALS OVER A FINITE-FIELD
BRAWLEY, JV
CARLITZ, L
[J]. DISCRETE MATHEMATICS, 1987, 65 (02) : 115 - 139
[2] A THEOREM OF DICKSON ON IRREDUCIBLE POLYNOMIALS
CARLITZ, L
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1952, 3 (05) : 693 - 700
[3] Lidl R., 1997, Encyclopedia of Mathematics and Its Applications, V20
[4] Mullen G. L., 2013, Handbook of Finite Fields
[5] A note on composed products of polynomials over finite fields
Stichtenoth, Henning
[J]. DESIGNS CODES AND CRYPTOGRAPHY, 2014, 73 (01) : 27 - 32

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