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

Splitting authentication codes with perfect secrecy: new results, constructions and connections with algebraic manipulation detection codes