Finite Euclidean Geometry Approach for Constructing Balanced Incomplete Block Design (BIBD)

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...

permutation approach for adjusted durbin rank test used in balanced incomplete block designs for tied data

durbin's rank test is widely used for testing treatment effects in balanced incomplete block designs (bibds)which have wide applications in sensory analysis. this test is failed for bibds when ties data occur. an adjusted version of durbin rank test for this kind of data is given to solve this problem. chi-square approximation, which is commonly used for this test, is not adequate for small bib...

Splitting balanced incomplete block designs

Low Density Parity Check Codes Based on Finite Geometries and Balanced Incomplete Block Design

Low Density Parity Check (LDPC) Codes are the class of linear block codes which provide near capacity performance on large collection of data transmission channels while simultaneously feasible for implementable decoders. LDPC codes were first proposed by Gallger in 1967 [1] and were rarely used until their rediscovery by Mackay, Luby and others [9][10][11]. Much research is devoted to characte...

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...