  We present several generalizations of results for splitting authentication
codes by studying the aspect of multi-fold security. As the two primary
results, we prove a combinatorial lower bound on the number of encoding rules
and a combinatorial characterization of optimal splitting authentication codes
that are multi-fold secure against spoofing attacks. The characterization is
based on a new type of combinatorial designs, which we introduce and for which
basic necessary conditions are given regarding their existence.
