Showing papers on "Orthogonal array published in 1970"

Orthogonal latin square codes

Abstract: A new class of multiple-error correcting codes has been developed. Since it belongs to the class of one-step-decodable majority codes, it can be decoded at an exceptionally high speed. This class of codes is derived from a set of mutually orthogonal Latin squares. This mutually orthogonal property provides a class of codes having a unique feature of "modularity." The parityc heck matrix possesses a uniform pattern and results in a small number of inputs to modulo 2 adders. This class of codes has m2 data bits, where m is an integer, and 2tm check bits for t-error correcting.

F-square and Orthogonal F-square Designs. A Generalization of Latin Squares and Orthogonal Latin Square Designs

Abstract: In this paper we are concerned with a generalization of the concept of Latin squares and orthogonality of Latin squares. The condition that every element appears once in each row and each column is replaced by the condition that it appears the same number of times in each row and each column. We call such squares $F$-squares. The usefulness of introducing and investigating the properties of $F$-squares could be justified in two directions. $F$-squares have meaningful applications in laying out experimental designs as exhibited previously by some authors. Their properties prove to be a useful tool in the studies of existence of orthogonal Latin squares and other combinatorial problems.

Experimental Designs and Combinatorial Systems Associated with Latin Squares and Sets of Mutually Orthogonal Latin Squares

Abstract: In this expository paper we have demonstrated the importance of the theory of Latin squares and mutually orthogonal Latin squares in the field of design of experiments and combinatorial analysis. It is shown that many well-known and important designs and/or combinatorial systems are either equivalent or can be derived from Latin squares or a set of mutually orthogonal Latin squares.

Empirical Equation of Neutron Diffusion System Application of the Experimental Design Technique

Abstract: An empirical equation between the cross sections and criticality factor was derived by the technique of experimental design and regression analysis. Factorial experiments taking account of interactions between factors was designed with use made of the orthogonal array. Numerical calculation of a two-group, two-core system was performed and an empirical equation derived by regression analysis, resulting in a criticality factor with acceptable accracy. The technique is general in nature. It should be applicable to learning control and optimum design of reactor systems.

Kirkman-Steiner Triple Systems and Sets of Mutually Orthogonal Latin Squares

Abstract: It is shown that every Kirkmai!--Steiner triple system of order v ;;; 3 (mod 6) implies the existence of a set consisting of at least one pair of mutually, orthogonal latin sq_uares of order v. The combinatorial structure of this set is different from those of known sets of orthogonal latin squares in the literature and this might prove to be useful for the construction of other designs and combinatorial systems derivable from sets of mutually orthogonal latin squares·. The case v = 15 leads to a new result, namely the existence of a set consisting of three mutually orthogonal latin sq_uares of order 15.