English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

An irreducible polynomial over $\Bbb F_q$ is said to be normal over $\BbbF_q$ if its roots are linearly independent over $\Bbb F_q$. We show that thereis a polynomial $h_n(X_1,\dots,X_n)\in\Bbb Z[X_1,\dots,X_n]$, independent of$q$, such that if an irreducible polynomial $f=X^n+a_1X^{n-1}+\cdots+a_n\in\BbbF_q[X]$ is such that $h_n(a_1,\dots,a_n)\ne 0$, then $f$ is normal over $\BbbF_q$. The polynomial $h_n(X_1,\dots,X_n)$ is computed explicitly for $n\le 5$and partially for $n=6$. When $\text{char}\,\Bbb F_q=p$, we also show thatthere is a polynomial $h_{p,n}(X_1,\dots,X_n)\in\Bbb F_p[X_1,\dots,X_n]$,depending on $p$, which is simpler than $h_n$ but has the same property. Theseresults remain valid for monic separable irreducible polynomials over anarbitrary field with a cyclic Galois group.

A Criterion for the Normality of Polynomials over Finite Fields Based on Their Coefficients