Weakly resolvable designs and unconditionally secure authentication codes.

摘要

A block design is said to be resolvable if the blocks can be partitioned into sets (resolutions) such that each element occurs once in each set, or in general (alpha)-resolvable if each element occurs exactly (alpha) times in each set. An (alpha)-resolvable design, (alpha) > 1, is said to be separable if one or more of the resolutions can be further partitioned into subsets each of which is also a resolution, and nonseparable otherwise. A design is affine if every block has the same number of elements in common with each block in the other resolutions. We introduce a new class of designs which we call weakly resolvable in which the blocks can be partitioned into sets such that each element occurs (alpha)(sub i) times in set i: (alpha)(sub i) not the same for all i, otherwise the design would be (alpha)-resolvable. The reason for the interest in weakly resolvable designs is that every nonseparable and affine weakly resolvable design corresponds in a natural way to a perfect and unconditionally secure authentication code that contains no proper subcode satisfying the same security requirements. 7 refs., 21 figs.