The combinatorics of authentication and secrecy codes

This paper is a study of the combinatorics of unconditionally secure secrecy and authentication codes, under the assumption that each encoding rule is to be used for the transmission of some numberL of successive messages. We obtain bounds on the number of encoding rules required in order to obtain maximum levels of security. Some constructions are also given for codes which have the minimum number of encoding rules. These constructions use various types of combinatorial designs.