  In this work, we derive upper bounds on the cardinality of tandem duplication
and palindromic deletion correcting codes by deriving the generalized sphere
packing bound for these error types. We first prove that an upper bound for
tandem deletions is also an upper bound for inserting the respective type of
duplications. Therefore, we derive the bounds based on these special deletions
as this results in tighter bounds. We determine the spheres for tandem and
palindromic duplications/deletions and the number of words with a specific
sphere size. Our upper bounds on the cardinality directly imply lower bounds on
the redundancy which we compare with the redundancy of the best known
construction correcting arbitrary burst errors. Our results indicate that the
correction of palindromic duplications requires more redundancy than the
correction of tandem duplications. Further, there is a significant gap between
the minimum redundancy of duplication correcting codes and burst insertion
correcting codes.
