# Maximal cyclic subgroups of the groups of units of Galois rings: a computational approach

Maximal cyclic subgroups of the groups of units of Galois rings: a computational approach We present a computational approach based on algorithmic techniques to obtain maximal cyclic subgroups of the groups of units in Galois rings. The objective of this work was to provide an automated methodology to obtain such maximal cyclic subgroups for minimizing the human effort in such calculations. Necessity of getting a stock of maximal cyclic subgroups is due to their novel role in the formation of cyclic codes over finite commutative rings and prophesied shifting of S-box construction through binary field extensions $$\mathrm{GF}( {2^h}),1\le h\le 8$$ GF ( 2 h ) , 1 ≤ h ≤ 8 to these maximal cyclic subgroups of the groups of units of finite Galois rings $$\mathrm{GR}(2^{k},{h})$$ GR ( 2 k , h ) . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational and Applied Mathematics Springer Journals

# Maximal cyclic subgroups of the groups of units of Galois rings: a computational approach

, Volume 36 (3) – Nov 5, 2015
25 pages

/lp/springer_journal/maximal-cyclic-subgroups-of-the-groups-of-units-of-galois-rings-a-gQhYUBWKZj
Publisher
Springer International Publishing
Subject
Mathematics; Applications of Mathematics; Computational Mathematics and Numerical Analysis; Mathematical Applications in the Physical Sciences; Mathematical Applications in Computer Science
ISSN
0101-8205
eISSN
1807-0302
D.O.I.
10.1007/s40314-015-0281-9
Publisher site
See Article on Publisher Site

### Abstract

We present a computational approach based on algorithmic techniques to obtain maximal cyclic subgroups of the groups of units in Galois rings. The objective of this work was to provide an automated methodology to obtain such maximal cyclic subgroups for minimizing the human effort in such calculations. Necessity of getting a stock of maximal cyclic subgroups is due to their novel role in the formation of cyclic codes over finite commutative rings and prophesied shifting of S-box construction through binary field extensions $$\mathrm{GF}( {2^h}),1\le h\le 8$$ GF ( 2 h ) , 1 ≤ h ≤ 8 to these maximal cyclic subgroups of the groups of units of finite Galois rings $$\mathrm{GR}(2^{k},{h})$$ GR ( 2 k , h ) .

### Journal

Computational and Applied MathematicsSpringer Journals

Published: Nov 5, 2015

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly ### Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. ### Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations