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Abstract: The branch group of a strongly controllable group code is a shift group. Weshow that a shift group can be characterized in a very simple way. In additionit is shown that if a strongly controllable group code is labeled with Latinsquares, a strongly controllable Latin group code, then the shift group issolvable. Moreover the mathematical structure of a Latin square as atranslation net and the shift group of a strongly controllable Latin groupcode are closely related. Thus a strongly controllable Latin group code can beviewed as a natural extension of a Latin square to a sequence space. Lastly weconstruct shift groups. We show that it is sufficient to construct a simplergroup, the state group of a shift group. We give an algorithm to find the stategroup, and from this it is easy to construct a stronlgy controllable Latingroup code.



Author: Kenneth M. Mackenthun Jr

Source: https://arxiv.org/







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