Tsallis entropy as a lower bound of average description length for the q-generalized code tree

We prove that the generalized Shannon additivity determines a lower bound of average description length for the q-generalized Z3-ary code tree. To clarify our main result, at first it is shown that the original Shannon additivity determines a lower bound of average code length of a Z3-ary code tree. As its generalization, we present our main result mentioned above. The generalized Shannon additivity is one of the generalized Shannon-Khinchin axioms for Tsallis entropy, i.e. one-parameter generalization of Shannon entropy. This reveals that Tsallis entropy is a lower bound of average description length for the q-generalized Z3-ary code tree.