2008/02/19 by Kenneth M. Mackenthun, Kenneth M. Mackenthun Jr, Mackenthun, Kenneth M.
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Cellular Automata and Applications #Coding theory and cryptography #DNA and Biological Computing #E.4 #FOS: Computer and information sciences #H.1.1 #Information Theory (cs.IT) #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.0802.2723
Improved algorithm included and paper rewritten; 26 pages
openalex publication_date 2008/02/19 · arxiv created 2008/10/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.