On a multiplicative order of Gauss periods and related questions
Roman Popovych
TL;DR
This paper establishes explicit lower bounds on the multiplicative order of generalized Gauss period elements, improving previous bounds in certain cases, which enhances understanding of their algebraic properties.
Contribution
It provides new explicit lower bounds for the multiplicative order of elements related to Gauss periods, extending and refining prior results.
Findings
Improved lower bounds for multiplicative orders of Gauss period elements
Enhanced understanding of algebraic properties of these elements
Partial case bounds surpass previous results
Abstract
We obtain explicit lower bounds on multiplicative order of elements that have more general form than finite field Gauss period. In a partial case of Gauss period this bound improves the previous bound of O.Ahmadi, I.E.Shparlinski and J.F.Voloch
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Taxonomy
TopicsCoding theory and cryptography · Finite Group Theory Research · Cryptography and Residue Arithmetic