Divisible Designs Research Articles

Key Pre-distribution Schemes via Certain Resolvable Block Designs

Earlier optimal key pre\(-\)distribution schemes (KPSs) for distributed sensor networks (DSNs) were proposed using combinatorial designs via transversal designs, affine, and partially affine resolvable designs. Here, nearly optimal KPSs are introduced and a class of such KPSs is obtained from resolvable group divisible designs. These KPSs are nearly optimal in the sense of local connectivity. A metric for the efficiency of KPSs is given. Further, an optimal KPS has also been proposed using affine resolvable \( L_{2} \)-type design.

A Survey on Partially Resolvable Solutions of Regular Group Divisible Designs

A Survey on Partially Resolvable Solutions of Regular Group Divisible Designs

On Constructions of GMGDs

Modified group divisible designs MGD ( k , λ , m , n ) are extensively studied because of an intriguing combinatorial structure that they possess and their applications. In this paper, we present a generalization of MGDs called GMGD ( k , λ 1 , λ 2 , m , n ) , and we provide some elementary results and constructions of some special cases of GMGDs. In addition, we show that the necessary conditions are sufficient for the existence of a GMGD ( 3 , λ , 2 λ , m , n ) for any positive integer λ , and a GMGD ( 3 , 2 , 3 , m , n ) . Though not a general result, the construction of a GMGD ( 3 , 3 , 2 , 2 , 6 ) given in the paper is worth mentioning in the abstract. Along with another example of a GMGD ( 3 , 3 , 2 , 2 , 4 ) , and n to t n construction, we have families of GMGD ( 3 , 3 λ , 2 λ , 2 , n ) s for n = 4 t or 6 t when t ≡ 0 , 1 ( mod 3 ) , for any positive integer λ .

Group divisible designs with block size 4 and group sizes 4 and 7

AbstractIn this paper, we consider the existence of group divisible designs (GDDs) with block size and group sizes and . We show that there exists a ‐GDD of type for all but a finite specified set of feasible values for .

Block Structured Hadamard matrices from certain arrays

We have constructed Block structured Hadamard matrices in which odd number of blocks are used in a row (column). These matrices are different than those introduced by Agaian. Generalised forms of arrays developed by Goethals-Seidel, Wallis-Whiteman and Seberry-Balonin heve been employed. Such types of matrices are applicable in the constructions of nested group divisible designs.

Strongly regular graphs decomposable into a divisible design graph and a Hoffman coclique

Strongly regular graphs decomposable into a divisible design graph and a Hoffman coclique

3-Group Divisible Designs with 3 Groups and Block Size 5

A 3 -GDD ( n , 2 , k , λ 1 , λ 2 ) was defined by combining the definitions of a group divisible design and a t-design. In this paper, we extend the definitions to 3 groups and block size 5, and we denote such GDD by 3 -GDD ( n , 3 , 5 , μ 1 , μ 2 ). Some necessary conditions for the existence of these GDDs are developed, and several new constructions and specific instances of nonexistence are given.

Frames and Doubly Resolvable Group Divisible Designs with Block Size Three and Index Two

Frames and Doubly Resolvable Group Divisible Designs with Block Size Three and Index Two

Student Egocentric Control through the Student Team Achievement Division Design

Student Egocentric Control through the Student Team Achievement Division Design

A generalization of group divisible t $t$‐designs

AbstractCameron defined the concept of generalized ‐designs, which generalized ‐designs, resolvable designs and orthogonal arrays. This paper introduces a new class of combinatorial designs which simultaneously provide a generalization of both generalized ‐designs and group divisible ‐designs. In certain cases, we derive necessary conditions for the existence of generalized group divisible ‐designs, and then point out close connections with various well‐known classes of designs, including mixed orthogonal arrays, factorizations of the complete multipartite graphs, large sets of group divisible designs, and group divisible designs with (orthogonal) resolvability. Moreover, we investigate constructions for generalized group divisible ‐designs and almost completely determine their existence for and small block sizes.

Design of time division multiplexing/wavelength division multiplexing passive optical network system for high-capacity network

This paper presents the design of time division multiplexing-wavelength division multiplexing-passive optical network (TDM-WDM PON). In this design, the current TDM PON is incorporated with the proposed WDM-PON in order to design a high-capacity network with lower loss requirements. The design has been simulated using OptiSystem software. The upstream wavelength for WDM is between 1,530.334 to 1,542.142 nm while for TDM is 1,310 nm. The downstream wavelength for WDM is from 1,569.865 to 1,581.973 nm, while for TDM is 1,490 nm. Based on the result, it is found that the proposed network is capable to support up to 64 customers with a bit rate of 2.5 Gbps.

On the existence of k $k$‐cycle semiframes for even k $k$

AbstractA ‐semiframe of type is a ‐group divisible design of type in which is the vertex set, is the group set, and the set of ‐cycles can be written as a disjoint union where is partitioned into parallel classes on and is partitioned into holey parallel classes, each parallel class or holey parallel class being a set of vertex disjoint cycles whose vertex sets partition or for some . In this paper, we almost completely solve the existence of a ‐semiframe of type for all and a ‐semiframe of type for all and .

Optimal key pre‐distribution schemes from affine resolvable and partially affine resolvable designs

AbstractVarious key pre‐distribution schemes (KPSs) for distributed sensor networks (DSNs) were obtained from different combinatorial designs. A block design may be mapped to a KPS where is the number of nodes or network size and is the number of keys (points) per node. A KPS is corresponding to a symmetric balanced incomplete block design has full connectivity where all nodes are connected to each other. But it is desirable that all nodes do not share common keys as the compromise of any node will destroy the whole network (see Lee & Stinson, 2005; Martin, 2009). To meet the situation, Lee and Stinson (2005) introduced μ—common intersection design which has disjoint blocks and these disjoint blocks can establish a secure communication through certain common intersecting blocks. Here we have proposed optimal KPSs from affine resolvable and partially affine resolvable balanced incomplete block designs, group divisible designs and L2—type designs. It is shown that these designs are important classes of μ—common intersection designs. The KPSs obtained here are optimal in the sense of local connectivity. Mathematics Subject Classification (2010): 94C30; 68R05; 05B05; 62K10.

A New Construction of Strongly Regular Graphs with Parameters of the Complement Symplectic Graph

The symplectic graph $Sp(2d, q)$ is the collinearity graph of the symplectic space of dimension $2d$ over the finite field of order $q$. A $k$-regular graph on $v$ vertices is a divisible design graph with parameters $(v,k,\lambda_1,\lambda_2,m,n)$ if its vertex set can be partitioned into $m$ classes of size $n$, such that any two different vertices from the same class have $\lambda_1$ common neighbours, and any two vertices from different classes have $\lambda_2$ common neighbours whenever it is not complete or edgeless. In this paper we propose a new construction of strongly regular graphs with the parameters of the complement of the symplectic graph using divisible design graphs.

Joint Beamforming Design for Intelligent Omni Surface Assisted Wireless Communication Systems

Intelligent reflecting surface (IRS) has been widely considered as one of the key enabling techniques for future wireless communication networks owing to its ability of dynamically controlling the phase shift of reflected electromagnetic (EM) waves to construct a favorable propagation environment. While IRS only focuses on signal reflection, the recently emerged innovative concept of intelligent omni-surface (IOS) can provide the dual functionality of manipulating reflecting and transmitting signals. Thus, IOS is a new paradigm for achieving ubiquitous wireless communications. In this paper, we consider an IOS-assisted multi-user multi-input single-output (MU-MISO) system where the IOS utilizes its reflective and transmissive properties to enhance the MU-MISO transmission. Both power minimization and sum-rate maximization problems are solved by exploiting the second-order cone programming (SOCP), Riemannian manifold, weighted minimum mean square error (WMMSE), and block coordinate descent (BCD) methods. Simulation results verify the advancements of the IOS for wireless systems and illustrate the significant performance improvement of our proposed joint transmit beamforming, reflecting and transmitting phase-shift, and IOS energy division design algorithms. Compared with conventional IRS, IOS can significantly extend the communication coverage, enhance the strength of received signals, and improve the quality of communication links.

Design and analysis of a frequency division and duty cycle control circuit for on-chip signal synthesis

In this article, a complementary metal–oxide–semiconductor (CMOS) frequency and duty cycle controller (FDCC) is presented for on-chip signal synthesis. The circuit consists of a few logic gates and a voltage-controlled oscillator, and is functionally similar to a programmable divide-by-N frequency divider. It is designed for driving integrated sensor and actuator systems. Compared with other frequency dividers with the same control flexibility, the proposed circuit features a compact topology and allows the control over the output signal duty cycle. For the proof-of-concept, a prototype 1 × 4 array of identical FDCCs has been fabricated on a 0.35μm Austria Mikro Systeme (AMS) CMOS process. Each FDCC occupies an active area of 0.0051mm2, which is area-efficient. The array has been validated to generate 4 synchronized 4MHz∼64MHz outputs with a duty cycle tuning range of 3.125%∼96.875%. Although driven by a 5-V power supply, it still provides a relatively high power-efficiency of 1.26GHz/mW.

Design and Implementation of High-Linearity Wavelength Division Multiplexing Analog Optical Link

Design and Implementation of High-Linearity Wavelength Division Multiplexing Analog Optical Link

Algebraic constructions of group divisible designs

Some series of Group divisible designs using generalized Bhaskar Rao designs over Dihedral, Symmetric and Alternating groups are obtained.

Group divisible designs with block size 4 where the group sizes are congruent to 1 mod 3

In this paper we consider the existence of 4-GDDs on v points with v≤50. We consider the case v≡1(mod3) and construct designs for all feasible group types here. We also enumerate all 4-GDDs with type 74 and compare the actions of their automorphism groups. When v≡0(mod3) and v≤50, there are no feasible group types for which existence has not been determined, but for v≡2(mod3) and v≤50, we obtain 4-GDDs for two more feasible group types.

Design and Performance Analysis of DWDM-PON

This paper presents on the design and analysis of Dense Wavelength Division Multiplexing Passive Optical Network (DWDM-PON) which is the upcoming trend technology nowadays to transmit up to 40 Gbps data. Various modulation techniques such as Non-Return Zero (NRZ), Return-Zero (RZ) and duo binary coding are simulated in this DWDM-PON. Using OptiSystem software, DWDM-PON is designed and simulated for 32 channels with spacing of 100 GHz and bit rate of 10 Gbps. An Erbium Doped Fiber Amplifier (EDFA) and Dispersion - Compensating Fiber (DCF) is deployed in the DWDM design. It is found that duo binary modulation technique gives the best performance with minimum BER of 2.66x10-19. From the simulation result, it also found that the proposed DWDM PON design is suitable to be deployed for current network.