On the Balanced Incomplete Block Design for Rankings

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...

Remarks on Balanced Incomplete Block Designs

Proof. Assume the hypothesis and the falsity of either conclusion. Construct matrix A of 2x + 2 rows and 4x+4 columns, with entries + 1 and — 1. The first column contains exclusively +1, and the second column — 1. Set up one-to-one correspondences between rows of A and elements of D ; between columns other than the first two of A and blocks of D. Enter +1 if the element is contained in the bloc...

Splitting balanced incomplete block designs

Beautifully Ordered Balanced Incomplete Block Designs

Beautifully Ordered Balanced Incomplete Block Designs, BOBIBD(v, k, λ, k1, λ1), are defined and the proof is given to show that necessary conditions are sufficient for the existence of BOBIBD with block size k=3 and k1=2 and for k=4 and k1=2 except possibly for eleven exceptions. Existence of BOBIBDs with block size k=4 and k1=3 is demonstrated for all but one infinite family and the non-existe...