An Incomplete Block Change-Over Design Balanced for First and Second-Order Residual Effect

Calculating Balanced Incomplete Block Design for Educational Assessments

A popular design in large scale' educational assessments is the balanced incomplete block design. The design assumes that the item pool is split into a set of blocks of items that are assigned to assessment booklets. This paper shows how the technique of 0-1 linear programming can be used to calculate a balanced incomplete block design. Several structural as well as practical constraints on thi...

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...

Splitting balanced incomplete block designs

Computer Aided First- and Second-Order Triangular Balanced Designs

Veevers and Boffey [1] identified 12 elementary balanced arrays. Zafar-Yab [2] confirmed the results of Veevers and Boffey [1] and investigated that among those 12 arrays, six arrays are unique and the other six are their associate partners. In this paper, there are 54 isomorphic classes containing 43-hills. Among these arrays 12 are vertically self-buildable arrays, after suitably augmentation...

Second-order balanced truncation

We consider second-order linear time-invariant systems. The objective of this paper is to present a new method for constructing a reduced system by preserving the second-order structure of the original system. This new model reduction method uses a variant of the well-known balanced truncation technique applied to second-order gramians. We also compare it with another existing technique. © 2004...