  A splitting BIBD is a type of combinatorial design that can be used to
construct splitting authentication codes with good properties. In this paper we
show that a design-theoretic approach is useful in the analysis of more general
splitting authentication codes. Motivated by the study of algebraic
manipulation detection (AMD) codes, we define the concept of a group generated
splitting authentication code. We show that all group-generated authentication
codes have perfect secrecy, which allows us to demonstrate that algebraic
manipulation detection codes can be considered to be a special case of an
authentication code with perfect secrecy.
  We also investigate splitting BIBDs that can be "equitably ordered". These
splitting BIBDs yield authentication codes with splitting that also have
perfect secrecy. We show that, while group generated BIBDs are inherently
equitably ordered, the concept is applicable to more general splitting BIBDs.
For various pairs $(k,c)$, we determine necessary and sufficient (or almost
sufficient) conditions for the existence of $(v, k \times c,1)$-splitting BIBDs
that can be equitably ordered. The pairs for which we can solve this problem
are $(k,c) = (3,2), (4,2), (3,3)$ and $(3,4)$, as well as all cases with $k =
2$.
