@inproceedings{ceb966c99d2c431ca4d92f12583dc722,

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

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.",

keywords = "Composed product, Finite field, Irreducible polynomial",

author = "Akihiro Munemasa and Hiroko Nakamura",

note = "Funding Information: A. Munemasa—The work of this author is partially supported by JSPS KAKENHI Grant Number 26400003. Publisher Copyright: {\textcopyright} Springer International Publishing AG 2016.; 6th International Workshop on Arithmetic of Finite Fields, WAIFI 2016 ; Conference date: 13-07-2016 Through 15-07-2016",

year = "2017",

doi = "10.1007/978-3-319-55227-9_7",

language = "English",

isbn = "9783319552262",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "84--92",

editor = "Sylvain Duquesne and Svetla Petkova-Nikova",

booktitle = "Arithmetic of Finite Fields - 6th International Workshop, WAIFI 2016, Revised Selected Papers",

}