Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Normal Bases on Galois Ring Extensions

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.

Journal reference: Symmetry 2018, 10, 702
DOI: 10.3390/sym10120702

## 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

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

Views 0