Existence of primitive pairs with two prescribed traces over finite fields
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Published:2023-07-21
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Volume:
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ISSN:0219-4988
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Container-title:Journal of Algebra and Its Applications
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language:en
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Short-container-title:J. Algebra Appl.
Author:
Choudhary Aakash1,
Sharma R. K.1
Affiliation:
1. Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, 110016, India
Abstract
Given [Formula: see text], a field with [Formula: see text] elements, where [Formula: see text] is a prime power and [Formula: see text] is a positive integer. Let [Formula: see text] and [Formula: see text] is a rational function, where [Formula: see text] and [Formula: see text] are distinct irreducible polynomials with [Formula: see text] in [Formula: see text]. We construct a sufficient condition on [Formula: see text] which guarantees primitive pairing [Formula: see text] exists in [Formula: see text] such that [Formula: see text] and [Formula: see text] for any prescribed [Formula: see text]. Further, we demonstrate for any positive integer [Formula: see text], such a pair definitely exists for large [Formula: see text]. The scenario when [Formula: see text] is handled separately and we verified that such a pair exists for all [Formula: see text] except from possible 71 values of [Formula: see text]. A result for the case [Formula: see text] is given as well.
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Algebra and Number Theory