On strongly controllable group codes and mixing group shifts: solvable groups, translation nets, and algorithms
Abstract
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.
Cite
@article{arxiv.0802.2723,
title = {On strongly controllable group codes and mixing group shifts: solvable groups, translation nets, and algorithms},
author = {Kenneth M. Mackenthun},
journal= {arXiv preprint arXiv:0802.2723},
year = {2008}
}
Comments
Improved algorithm included and paper rewritten; 26 pages