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- Title
Maximal cyclic subgroups of the groups of units of Galois rings: a computational approach.
- Authors
Shah, Tariq; Mehmood, Nasir; Andrade, Antonio; Palazzo, Reginaldo
- 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 $$\mathrm{GF}( {2^h}),1\le h\le 8$$ to these maximal cyclic subgroups of the groups of units of finite Galois rings $$\mathrm{GR}(2^{k},{h})$$ .
- Subjects
CYCLIC groups; GALOIS rings; MAXIMAL functions; COMPUTATIONAL complexity; COMPUTER algorithms; CYCLIC codes
- Publication
Computational & Applied Mathematics, 2017, Vol 36, Issue 3, p1273
- ISSN
0101-8205
- Publication type
Article
- DOI
10.1007/s40314-015-0281-9