CONSTRUCTION OF A NEW SERIES OF BALANCED INCOMPLETE BLOCK DESIGN

Construction of Balanced Incomplete Block Designs Using Cyclic Shifts

The construction of balanced incomplete block designs is considered using the method of cyclic shifts. An interesting feature of this method is that there is no need to construct the bocks of the actual design to obtain the properties of a design. One can obtain the off-diagonal elements of the concurrence matrix from the sets of shifts with less effort. A catalogue of balanced incomplete block...

A New Family of Partially Balanced Incomplete Block Designs with Some Latin Square Design Properties

Splitting balanced incomplete block designs

Minimum embedding of a P4-design into a balanced incomplete block design of index lambda

Let H be a subgraph of G. An H-design (V, C) of order v and index μ is embedded into a G-design (X,B) of order v + w and index λ if μ ≤ λ, V ⊆ X and there is an injective mapping f : C → B such that B is subgraph of f (B) for every B ∈ C. For every pair of positive integers v, λ, (except when λ = 3 and v = 30, 34, 42, 46, 54, 58, 66 or λ = 5 and v = 19) we determine the minimum value of w such ...

Self-Dual Codes and the (22,8,4) Balanced Incomplete Block Design

We enumerate a list of 594 inequivalent binary (33, 16) doubly-even self-orthogonal codes that have no all-zero coordinates along with their automorphism groups. It is proven that if a (22, 8, 4) Balanced Incomplete Block Design were to exist then the 22 rows of its incident matrix will be contained in at least one of the 594 codes. Without using computers, we eliminate this possibility for 116...