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## Acta Arithmetica

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## Enumeration of a special class of irreducible polynomials in characteristic 2

### Tom 194 / 2020

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

#### Streszczenie

$A$-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.

#### Autorzy

Faculty of Arts and Sciences
Boğaziçi University
34342 Bebek, İstanbul, Turkey
e-mail