Dembowski-Ostrom polynomials and Dickson polynomials

Sartaj Ul Hasan; Mohit Pal

doi:10.3934/amc.2022068

Article Contents

2024, Volume 18, Issue 4: 1084-1099. Doi: 10.3934/amc.2022068

This issue Previous Article Weierstrass semigroups on the third function field in a tower attaining the Drinfeld-Vlăduţ bound Next Article Cyclic codes over rings of matrices

Dembowski-Ostrom polynomials and Dickson polynomials

Sartaj Ul Hasan^1, and
Mohit Pal^2, ,

1.
Department of Mathematics, Indian Institute of Technology Jammu, Jammu 181221, India
2.
Department of Informatics, University of Bergen, PB 7803, 5020, Bergen, Norway

^*Corresponding author: Mohit Pal
^*Corresponding author: Mohit Pal

Received: May 2021

Revised: July 2022

Early access: September 2022

Published: August 2024

The first named author was partially supported during the course of this work by Start-up Research Grant SRG/2019/000295 from the Science and Engineering Research Board, Government of India, while he is currently supported by MATRICS Grant MTR/2019/000744 from the same organization

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Abstract

We give a complete classification of Dembowski-Ostrom polynomials from the composition of Dickson polynomials of arbitrary kind and monomials over finite fields. Moreover, by using a variant of the Weil bound for the number of points of affine algebraic curves over finite fields, we discuss the planarity of the obtained Dembowski-Ostrom polynomials.

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Mathematics Subject Classification: Primary: 12E20, 11T06; Secondary: 05A10.

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References

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