A 2 -code = Aane Resolvable + Bibd
نویسنده
چکیده
We say that an A 2-code is optimum if it has the minimum cheating probabilities and the minimum sizes of keys. We rst show that an optimum A 2-code implies an aane-resolvable design. Next, we de-ne an aane-resolvable + BIBD design and prove that an optimum A 2-code is equivalent to an aane-resolvable + BIBD design.
منابع مشابه
Combinatorial Classiication of Optimal Authentication Codes with Arbitration Satoshi Obana and Kaoru Kurosawa
Unconditionally secure authentication codes with arbitration (A 2-codes) protect against deceptions from the transmitter and the receiver as well as that from the opponent. We rst show that an optimal A 2-code implies an orthogonal array and an aane-resolvable design. Next we deene a new design, an aane-resolvable + BIBD, and prove that optimal A 2-codes are equivalent to this new design. From ...
متن کاملOn balanced incomplete-block designs with repeated blocks
Balanced incomplete-block designs (BIBDs) with repeated blocks are studied and constructed. We continue work initiated by van Lint and Ryser in 1972 and pursued by van Lint in 1973. We concentrate on constructing (v, b, r, k, λ)-BIBDs with repeated blocks, especially those with gcd(b, r, λ) = 1 and r ≤ 20. We obtain new bounds for the multiplicity of a block in terms of the parameters of a BIBD...
متن کاملThe Existence of DNR ( mt + 1 , m , m − 1 ) - BIBDs
A (v, m, m − 1)-BIBD D is said to be near resolvable (NRBIBD) if the blocks of D can be partitioned into classes R1, R2, . . . , Rv such that for each point x of D, there is precisely one class having no block containing x and each class contains precisely v − 1 points of the design. If an (v, m, λ)-NRBIBD has a pair of orthogonal resolutions, it is said to be doubly resolvable and is denoted D...
متن کاملA new look at an old construction: Constructing (simple) 3-designs from resolvable 2-designs
In 1963, Shrikhande and Raghavarao [5] published a recursive construction for designs that starts with a resolvable design (the “master design”) and then uses a second design (“the indexing design”) to take certain unions of blocks in each parallel class of the master design. Several variations of this construction have been studied by different authors. We revisit this construction, concentrat...
متن کاملThe Existence of Kirkman Squares-Doubly Resolvable (v, 3, 1)-BIBDs
A Kirkman square with index λ, latinicity μ, block size k, and v points, KSk(v; μ, λ), is a t × t array (t = λ(v − 1)/μ(k − 1)) defined on a v-set V such that (1) every point of V is contained in precisely μ cells of each row and column, (2) each cell of the array is either empty or contains a k-subset of V , and (3) the collection of blocks obtained from the non-empty cells of the array is a (...
متن کامل