A primitive normal pair with prescribed prenorm
K. Chatterjee, S.K. Tiwari

TL;DR
This paper establishes conditions for the existence of primitive normal pairs with prescribed prenorm in finite fields, extending previous results and providing nearly complete existence results for specific parameters.
Contribution
It introduces new sufficient conditions for primitive normal pairs with prescribed prenorm in finite fields, including nearly complete existence results for certain parameters.
Findings
Existence of primitive normal pairs under new conditions
Almost all pairs exist for specified parameters with few exceptions
Provides a framework for constructing such pairs with prescribed prenorm
Abstract
For any positive integers , , with being a prime power and , we establish a condition sufficient to ensure the existence of a primitive normal pair in over such that , where is prescribed. Here is a rational function subject to some minor restrictions such that deg()+deg() and . Finally, we conclude that for , , and where , such a pair will exist certainly for all except possibly choices at most.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsConnective tissue disorders research · semigroups and automata theory · Fuzzy and Soft Set Theory
