We give new combinatorial constructions for codes providing authentication
and secrecy for equiprobable source probability distributions. In particular,
we construct an infinite class of optimal authentication codes which are
multiple-fold secure against spoofing and simultaneously achieve perfect
secrecy. Several further new optimal codes satisfying these properties will
also be constructed and presented in general tables. Almost all of these appear
to be the first authentication codes with these properties.Comment: 5 pages (double-column); to appear in Proc. IEEE International
Symposium on Information Theory (ISIT 2009, Seoul, South Korea