Constructions Of External Difference Families

In the investigation of authentication codes, Ogata. Kurosawa. Stinson and Saido[W. Ogata, K. Kurosawa, D. R. Stinson and H. Saido, New combinatorial designs andtheir applications to authentication codes and secret, sharing schemes, Discrete Math.,2004, 279, 383-405] introduced the notion of external difference families(EDFs), andused EDFs to construct c-splitting A-codes. Both the impersonation attack proba-bility and substitution attack probability of the A-codes from an EDF achieve theirinformation-theoretic lower bounds. This article investigates the constructions of exter-nal difference families (v, u×c.λ)-EDFs, and gives the spectrum of (v, 2×c,λ)-EDFsfor c=2,3,4.