Topic
Combinatorial design
About: Combinatorial design is a research topic. Over the lifetime, 744 publications have been published within this topic receiving 15509 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: Balanced Incomplete Block Designs and t-Designs2-(v,k,l) Designs of Small OrderBIBDs with Small Block Sizet-designs, t = 3Steiner SystemsSymmetric DesignsResolvable and Near Resolvable DesignsLatin Squares, MOLS, and Orthogonal ArraysLatin SquareMutually Orthogonomic Latin Squares (MOLS)Incomplete MOLsOrthogonal ARrays of Index More Than OneOrthoghonal Array of Strength More Than TwoPairwise Balanced Designs
Abstract: Balanced Incomplete Block Designs and t-Designs2-(v,k,l) Designs of Small OrderBIBDs with Small Block Sizet-Designs, t = 3Steiner SystemsSymmetric DesignsResolvable and Near Resolvable DesignsLatin Squares, MOLS, and Orthogonal ArraysLatin SquaresMutually Orthogonal Latin Squares (MOLS)Incomplete MOLSOrthogonal Arrays of Index More Than OneOrthogonal Arrays of Strength More Than TwoPairwise Balanced DesignsPBDs and GDDs: The BasicsPBDs: Recursive ConstructionsPBD-ClosurePairwise Balanced Designs as Linear SpacesPBDs and GDDs of Higher IndexPBDs, Frames, and ResolvabilityOther Combinatorial DesignsAssociation SchemesBalanced (Part) Ternary DesignsBalanced Tournament DesignsBhaskar Rao DesignsComplete Mappings and Sequencings of Finite GroupsConfigurationsCostas ArraysCoveringsCycle SystemsDifference FamiliesDifference MatricesDifference Sets: AbelianDifference Sets: NonabelianDifference Triangle SetsDirected DesignsD-Optimal MatricesEmbedding Partial QuasigroupsEquidistant Permutation ArraysFactorial DesignsFrequency SquaresGeneralized QuadranglesGraph Decompositions and DesignsGraphical DesignsHadamard Matrices and DesignsHall Triple SystemsHowell DesignsMaximal Sets of MOLSMendelsohn DesignsThe Oberwolfach ProblemOrdered Designs and Perpendicular ArraysOrthogonal DesignsOrthogonal Main Effect PlansPackingsPartial GeometriesPartially Balanced Incomplete Block DesignsQuasigroupsQuasi-Symmetric Designs(r,l)-DesignsRoom SquaresSelf-Orthogonal Latin Squares (SOLS)SOLS with a Symmetric Orthogonal Mate (SOLSSOM)Sequences with Zero AutocorrelationSkolem SequencesSpherical t-DesignsStartersTrades and Defining Sets(t,m,s)-NetsTuscan Squarest-Wise Balanced DesignsUniformly Resolvable DesignsVector Space DesignsWeighing Matrices and Conference MatricesWhist TournamentsYouden Designs, GeneralizedYouden SquaresApplicationsCodesComputer Science: Selected ApplicationsApplications of Designs to CryptographyDerandomizationOptimality and Efficiency: Comparing Block DesignsGroup TestingScheduling a TournamentWinning the LotteryRelated Mathematics and Computational MethodsFinite Groups and DesignsNumber Theory and Finite FieldsGraphs and MultigraphsFactorizations of GraphsStrongly Regular GraphsTwo-GraphsClassical GeometriesProjective Planes, NondesarguesianComputational Methods in Design TheoryIndex
2,067 citations
Book•
17 Oct 2003TL;DR: It is shown here how orthogonal Latin squares can be transformed into BIBDs using Hadamard matrices, and how different sets and automorphisms can be modified for different levels of integration.
Abstract: Introduction to BIBDs.- Symmetric BIBDs.- Difference sets and automorphisms.- Hadamard matrices and designs.- Resolvable BIBDs.- Steiner triple systems.- Mutually orthogonal Latin squares.- Pairwise balanced designs.- t-designs.- Orthogonal arrays and codes.- Index.
590 citations
Book•
1 Jan 2008TL;DR: Theoretical Computer Science, Information Structures, and Networks and Flows.
Abstract: Foundations Counting Methods Sequences Number Theory Algebraic Structures Linear Algebra Discrete Probability Graph Theory Trees Networks and Flows Partially Ordered Sets Combinatorial Designs Discrete and Computational Geometry Coding Theory and Cryptology Discrete Optimization Theoretical Computer Science Information Structures Data Mining Bioinformatics
541 citations
TL;DR: Novel deterministic and hybrid approaches based on Combinatorial Design are presented for deciding how many and which keys to assign to each key-chain before the sensor network deployment to obtain efficient key distribution schemes.
Abstract: Secure communications in wireless sensor networks operating under adversarial conditions require providing pairwise (symmetric) keys to sensor nodes. In large scale deployment scenarios, there is no priory knowledge of post deployment network configuration since nodes may be randomly scattered over a hostile territory. Thus, shared keys must be distributed before deployment to provide each node a key-chain. For large sensor networks it is infeasible to store a unique key for all other nodes in the key-chain of a sensor node. Consequently, for secure communication either two nodes have a key in common in their key-chains and they have a wireless link between them, or there is a path, called key-path, among these two nodes where each pair of neighboring nodes on this path have a key in common. Length of the key-path is the key factor for efficiency of the design. This paper presents novel deterministic and hybrid approaches based on Combinatorial Design for deciding how many and which keys to assign to each key-chain before the sensor network deployment. In particular, Balanced Incomplete Block Designs (BIBD) and Generalized Quadrangles (GQ) are mapped to obtain efficient key distribution schemes. Performance and security properties of the proposed schemes are studied both analytically and computationally. Comparison to related work shows that the combinatorial approach produces better connectivity with smaller key-chain sizes.
491 citations
Book•
1 Jan 1992TL;DR: The standard geometric codes are presented, followed by a list of recommended designs and some examples of how these designs might be implemented in the real world.
Abstract: Algebraic coding theory has in recent years been increasingly applied to the study of combinatorial designs. This book gives an account of many of those applications together with a thorough general introduction to both design theory and coding theory - developing the relationship between the two areas. The first half of the book contains background material in design theory, including symmetric designs and designs from affine and projective geometry, and in coding theory, coverage of most of the important classes of linear codes. In particular, the authors provide a new treatment of the Reed-Muller and generalized Reed-Muller codes. The last three chapters treat the applications of coding theory to some important classes of designs, namely finite planes, Hadamard designs and Steiner systems, in particular the Witt systems. The book is aimed at mathematicians working in either coding theory or combinatorics - or related areas of algebra. The book is, however, designed to be used by non-specialists and can be used by those graduate students or computer scientists who may be working in these areas.
405 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 1 |
| 2024 | 6 |
| 2023 | 6 |
| 2022 | 19 |
| 2021 | 35 |
| 2020 | 29 |