On the construction of perfect authentication codes that permit arbitration

In English Authentication codes that permit arbitration are codes that unconditionally protect against deceptions from the outsiders and additionally also protect against some forms of deceptions from the insiders. Simmons introduced this authentication model and he also showed a way of constructing such codes, called the Cartesian product construction. We present a general way of constructing such codes and we also derive two specific classes of such codes. One that is perfect in the sense that it meets the lower bounds on the size of the transmitter’s and the receiver’s keys and one that allows the number of source states to be chosen arbitrarily large.