Combinatorial classification of optimal authentication codes with arbitration (Q1581793)

The paper deals with a combinatorial classification of optimal authentication codes with arbitration (\(A^2\)-codes). Previously such classification was known for usual authentication codes (\(A\)-codes), namely an optimal \(A\)-code is equivalent to a BIBD (balanced incomplete block design) and an optimal \(A\)-code without secrecy is equivalent to an orthogonal array. In the paper, a connection between \(A^2\)-codes and combinatorial designs is presented. The paper begins with a brief introduction followed by an overview of \(A^2\)-codes and a section devoted to block designs. In the next section, the authors show that if there exists an optimal \((l, c)\) \(A^2\)-code then there exists an orthogonal array and an affine \(c\)-resolvable design. Subsequently a new design, an affine \(c\)-resolvable + BIBD, is defined and it is shown that optimal \((l, c)\) \(A^2\)-codes are equivalent to this new design. Next, a condition on the parameters for the existence of optimal \((l, c)\) \(A^2\)-codes is derived. Finally, tighter lower bounds on the size of keys than before for large sizes of source states are presented.