Factoring linear trellises
David Conti, Boston, Nigel · Repository for Publications and Research Data (ETH Zurich) · 2012
Koetter/Vardy proved in [9] the remarkable result that any linear trellis can be factored into elementary trellises.We prove that the spans (and their multiplicities) of the elementary factors of a linear trellis are uniquely determined, extending a known result for minimal trellises ([4], [8], [11]).In doing so, we give a graphical method to compute all the spans and their multiplicities.We show also how to determine all the possible edge-labelings of the factors of a linear trellis, and give exact conditions for their uniqueness.These results can help to compute and classify all trellises for a given code.