A note on the Brawley-Carlitz theorem on irreducibility of composed products of polynomials over finite fields

Akihiro Munemasa, Hiroko Nakamura

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish
Title of host publicationArithmetic of Finite Fields - 6th International Workshop, WAIFI 2016, Revised Selected Papers
EditorsSylvain Duquesne, Svetla Petkova-Nikova
PublisherSpringer-Verlag
Pages84-92
Number of pages9
ISBN (Print)9783319552262
DOIs
Publication statusPublished - 2017 Jan 1
Event6th International Workshop on Arithmetic of Finite Fields, WAIFI 2016 - Ghent, Belgium
Duration: 2016 Jul 132016 Jul 15

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10064 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other6th International Workshop on Arithmetic of Finite Fields, WAIFI 2016
CountryBelgium
City Ghent
Period16/7/1316/7/15

Keywords

  • Composed product
  • Finite field
  • Irreducible polynomial

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Fingerprint Dive into the research topics of 'A note on the Brawley-Carlitz theorem on irreducibility of composed products of polynomials over finite fields'. Together they form a unique fingerprint.

  • Cite this

    Munemasa, A., & Nakamura, H. (2017). A note on the Brawley-Carlitz theorem on irreducibility of composed products of polynomials over finite fields. In S. Duquesne, & S. Petkova-Nikova (Eds.), Arithmetic of Finite Fields - 6th International Workshop, WAIFI 2016, Revised Selected Papers (pp. 84-92). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10064 LNCS). Springer-Verlag. https://doi.org/10.1007/978-3-319-55227-9_7