A+ CATEGORY SCIENTIFIC UNIT

PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Enumeration of a special class of irreducible polynomials in characteristic 2

Volume 194 / 2020

Alp Bassa, Ricardo Menares Acta Arithmetica 194 (2020), 51-57 MSC: Primary 11T55, 11R58; Secondary 14H05, 14Q05. DOI: 10.4064/aa190116-21-5 Published online: 31 January 2020

Abstract

$A$-polynomials were introduced by Meyn and play an important role in the iterative construction of high degree self-reciprocal irreducible polynomials over the field $\mathbb F_2$, since they constitute the starting point of the iteration. The exact number of $A$-polynomials of each degree was given by Niederreiter. Kyuregyan extended the construction of Meyn to arbitrary finite fields of characteristic 2. We relate the $A$-polynomials in this more general setting to inert places in a certain extension of elliptic function fields and obtain an explicit counting formula for their number. In particular, we are able to show that, with an isolated exception, there exist $A$-polynomials of every degree.

Authors

  • Alp BassaDepartment of Mathematics
    Faculty of Arts and Sciences
    Boğaziçi University
    34342 Bebek, İstanbul, Turkey
    e-mail
  • Ricardo MenaresFacultad de Matemáticas
    Pontificia Universidad Católica de Chile
    Vicuña Mackenna 4860
    Santiago, Chile
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image