Locally resolvable BIBDs and generalized quadrangles with ovoids

This article is in two main parts. The first gives some (q,k, 1) difference families with q a prime power and 7 ≤ k ≤ 9; it also gives some GD(k, 1, k,kq)s which are extendable to resolvable (kq,k, 1) BIBDs for k E {6,8,10} and q a prime power equal to 1 mod 2(k − 1). The second uses some of these plus several recursive constructions to obtain some new (v,k,, 1) BIBDs with 7 ≤ k ≤ 9 and some new (v,8,1) resolvable BIBDs. © 1996 John Wiley & Sons, Inc.

Resolvable bibd and sols

Group Divisible PBIBDs are important combinatorial structures with diverse applications. In this paper, we provided a construction technique for Group Divisible (v-1,k,0,1) PBIBDs. This was achieved by using techniques described in literature to construct Nim addition tables of order 2n, 2≤n≤5 and (k2,b,r,k,1)Resolvable BIBDs respectively. A “block cutting” procedure was thereafter used to generate corresponding Group Divisible (v-1,k,0,1) PBIBDs from the (k2,b,r,k,1)Resolvable BIBDs. These procedures were streamlined and implemented in MATLAB. The generated designs are regular with parameters(15,15,4,4,5,3,0,1);(63,63,8,8,9,7,0,1);(255,255,16,16,17,15,0,1) and (1023,1023,32,32,33,31,0,1). The MATLAB codes written are useful for generating the blocks of the designs which can be easily adapted and utilized in other relevant studies. Also, we have been able to establish a link between the game of Nim and Group Divisible (v-1,k,0,1) PBIBDs.

In a (v, k, λ: w) incomplete block design (IBD) (or PBD [v, {k, w*}. λ]), the relation v ≥ (k − 1)w + 1 must hold. In the case of equality, the IBD is referred to as a block design with a large hole, and the existence of such a configuration is equivalent to the existence of a λ‐resolvable BIBD(v − w, k − 1, λ). The existence of such configurations is investigated for the case of k = 5. Necessary and sufficient conditions are given for all v and λ ≢ 2 (mod 4), and for λ ≡ 2 mod 4 with 11 possible exceptions for v. © 1993 John Wiley & Sons, Inc.

Resolvable <i>BIBDs</i>

On Traceability Property of Linear Codes and Resolvable BIBDS

A few more Kirkman squares and doubly near resolvable BIBDs with block size 3

A characterization of Pseudo-Affine Designs and their Relation to a Problem of Cordes

In this paper we relate how Equidistant Constant Weight Codes and Different Combinatorial Structures like Resolvable Balanced Incomplete Block Designs (RBIBD) , Nested Balanced Incomplete Block Designs (NBIBD) and Linear Codes are related with each other and then show how these Combinatorial Structures can be used as 2-Traceable (TA) Code.

As known, multiplicative secret sharing schemes over Abelian groups play an important role in threshold cryptography, such as in threshold RSA signature schemes. In this paper we present a new approach for constructing multiplicative threshold schemes over finite Abelian groups, which generalises a scheme proposed by Blackburn, Burmester, Desmedt and Wild in Eurocrypt’96. Our method is based on a notion of multiple perfect hash families, which we introduce in this paper. We also give several constructions for multiple perfect hash families from resolvable BIBD, difference matrix and error-correcting code.

In this paper, we investigate the PBD‐closure of sets K with {7,13} ⊆ K ⊆ {7,13,19,25,31,37,43}. In particular, we show that ν ≡ 1 mod 6, ν ≥ 98689 implies ν ϵ B({7,13}). As an intermediate result, many new 13‐GDDs of type 13q and resolvable BIBD with block size 6 or 12 are also constructed. Furthermore, we show some elements to be not essential in a Wilson basis for the PBD‐closed set {ν: ν ≡ 1 mod 6, ν ≥ 7}. © 2007 Wiley Periodicals, Inc. J Combin Designs 15: 283–314, 2007

Resolvable BIBDs with block size 7 and index 6

The necessary conditions for the existence of a resolvable BIBD RB(k,λ; v) are λ(v − 1) = 0(mod k − 1) and v = 0(mod k). In this article, it is proved that these conditions are also sufficient for k = 8 and λ = 7, with at most 36 possible exceptions. © 1994 John Wiley &amp; Sons, Inc.

A new look at an old construction: Constructing (simple) 3-designs from resolvable 2-designs

Existence of resolvable BIBDs with k = 5 and λ = 4