Combinatorial Characterizations of Authentication Codes II

For any authentication code for k source states and v messages having minimum possible deception probabilities (namely, P d 0 = k=v and P d 1 = (k ? 1)=(v ? 1)), we show that there must be at least v encoding rules. (This can be thought of as an authentication-code analogue of Fisher's Inequality .) We derive several properties that an extremal code must satisfy, and we characterize the extremal codes for equiprobable source states as arising from symmetric balanced incomplete block designs. We also present an inn-nite class of extremal codes, in which the source states are not equiprobable, derived from aane planes.