On strongly controllable group codes and mixing group shifts: solvable groups, translation nets, and algorithms
| dc.creator | Mackenthun Jr, Kenneth M. | |
| dc.date | 2008-02-19 | |
| dc.date | 2008-10-06 | |
| dc.date.accessioned | 2026-07-07T10:07:18Z | |
| dc.date.available | 2026-07-07T10:07:18Z | |
| dc.description | The branch group of a strongly controllable group code is a shift group. We show that a shift group can be characterized in a very simple way. In addition it is shown that if a strongly controllable group code is labeled with Latin squares, a strongly controllable Latin group code, then the shift group is solvable. Moreover the mathematical structure of a Latin square (as a translation net) and the shift group of a strongly controllable Latin group code are closely related. Thus a strongly controllable Latin group code can be viewed as a natural extension of a Latin square to a sequence space. Lastly we construct shift groups. We show that it is sufficient to construct a simpler group, the state group of a shift group. We give an algorithm to find the state group, and from this it is easy to construct a stronlgy controllable Latin group code. | |
| dc.description | Improved algorithm included and paper rewritten; 26 pages | |
| dc.identifier | https://arxiv.org/abs/0802.2723 | |
| dc.identifier | http://arxiv.org/abs/0802.2723 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/170588 | |
| dc.subject | Information Theory | |
| dc.subject | E.4; H.1.1 | |
| dc.title | On strongly controllable group codes and mixing group shifts: solvable groups, translation nets, and algorithms | |
| dc.type | text |