Kuriki and Fuji-Hara (1994) introduced an (r, 2)-design with mutually balanced nested subdesigns ((r, 2)-design with MBN), which is equivalent to a balanced array of strength 2 with s symbols, and gave some constructions of such (r, 2)-designs. In this paper, we consider cyclic orthogonal and balanced arrays, and we give a cyclic version of the results obtained by them. Furthermore, we give a c...

The Orthogonal arrays are helpful in guiding the heuristic algorithms to obtain a good solution when applied to NP-hard problems. This chapter deals with a new variant of PSO named Orthogonal PSO (OPSO) for solving the multiprocessor scheduling problem. The objective of applying the orthogonal concept in the basic PSO algorithm is to enhance the performance when applied to the scheduling proble...

There are many nonisomorphic orthogonal arrays with parameters OA(s3, s2 + s+1, s, 2) although the existence of the arrays yields many restrictions. We denote this by OA(3, s) for simplicity. V.D. Tonchev showed that for even the case of s = 3, there are at least 68 nonisomorphic orthogonal arrays. The arrays that are constructed by the n−dimensional finite spaces have parameters OA(s, (s − 1)/...

H. Kharaghani, in "Arrays for orthogonal designs", J. Combin. Designs, 8 (2000), 166-173, showed how to use amicable sets of matrices to construct orthogonal designs in orders divisible by eight. We show how amicable orthogonal designs can be used to make amicable sets and so obtain infinite families of orthogonal designs in six variables in orders divisible by eight.

Orthogonal arrays (OAs) are basic combinatorial structures, which appear under various disguises in cryptology and the theory of algorithms. Among their applications are universal hashing, authentica-tion codes, resilient and correlation-immune functions, derandomization of algorithms, and perfect local randomizers. In this paper, we give new bounds on the size of orthogonal arrays using Delsar...

A k2m×n (0,1) matrix is called a binary orthogonal array of strength m if in any m columns of the matrix every one of the possible 2 ordered (0,1) m-tuples occurs in exactly k rows and no two rows are identical. In this paper, the enumeration of binary orthogonal arrays is studied, and a closed expression for the enumeration of binary orthogonal arrays of strength 1 is given using the inclusion...

To study orthogonal arrays and signed orthogonal arrays, Ray-Chaudhuri and Singhi (1988 and 1994) considered some module spaces. Here, using a linear algebraic approach we define an inclusion matrix and find its rank. In the special case of Latin squares we show that there is a straightforward algorithm for generating a basis for this matrix using the so-called intercalates. We also extend this...