Normal Bases on Galois Ring Extensions
preprint
OA: closed
CC-BY-4.0
Abstract
In this paper we study the normal bases for Galois ring extension ${{R}} / {Z}_{p^r}$ where ${R}$ = ${GR}$(pr, n). We present a criterion on normal basis for ${{R}} / {Z}_{p^r}$ and reduce this problem to one of finite field extension $\overline{R} / \overline{Z}_{p^r}=F_{q} / F_{p} (q=p^n)$ by Theorem 1. We determine all optimal normal bases for Galois ring extension.
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- europepmc
- last seen: 2026-05-19T01:45:01.086888+00:00
- unpaywall
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License: CC-BY-4.0