License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.AofA.2022.9
URN: urn:nbn:de:0030-drops-160958
URL: https://drops.dagstuhl.de/opus/volltexte/2022/16095/
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Gao, Zhicheng

Improved Error Bounds for the Number of Irreducible Polynomials and Self-Reciprocal Irreducible Monic Polynomials with Prescribed Coefficients over a Finite Field

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Abstract

A polynomial is called self-reciprocal (or palindromic) if the sequence of its coefficients is palindromic. In this paper we obtain improved error bounds for the number of irreducible polynomials and self-reciprocal irreducible monic polynomials with prescribed coefficients over a finite field. The improved bounds imply that self-reciprocal irreducible monic polynomials with degree 2d and prescribed 𝓁 leading coefficients always exist provided that 𝓁 is slightly less than d/2.

BibTeX - Entry

@InProceedings{gao:LIPIcs.AofA.2022.9,
  author =	{Gao, Zhicheng},
  title =	{{Improved Error Bounds for the Number of Irreducible Polynomials and Self-Reciprocal Irreducible Monic Polynomials with Prescribed Coefficients over a Finite Field}},
  booktitle =	{33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022)},
  pages =	{9:1--9:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-230-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{225},
  editor =	{Ward, Mark Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16095},
  URN =		{urn:nbn:de:0030-drops-160958},
  doi =		{10.4230/LIPIcs.AofA.2022.9},
  annote =	{Keywords: finite fields, irreducible polynomials, prescribed coefficients, generating functions, Weil bounds, self-reciprocal}
}

Keywords: finite fields, irreducible polynomials, prescribed coefficients, generating functions, Weil bounds, self-reciprocal
Collection: 33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022)
Issue Date: 2022
Date of publication: 08.06.2022


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