Article
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Normal Bases on Galois Ring Extensions
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Version 1
: Received: 27 September 2018 / Approved: 28 September 2018 / Online: 28 September 2018 (09:41:32 CEST)
A peer-reviewed article of this Preprint also exists.
Zhang, A.; Feng, K. Normal Bases on Galois Ring Extensions. Symmetry 2018, 10, 702. Zhang, A.; Feng, K. Normal Bases on Galois Ring Extensions. Symmetry 2018, 10, 702.
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.
Keywords
Galois ring; optimal normal basis; multiplicative complexity; finite field
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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