# Accession Number:

## AD0658468

# Title:

## ON THE CONSTRUCTION OF ORTHOGONALIZED SQUARES BY FINITE FIELDS.

# Descriptive Note:

## Professional paper,

# Corporate Author:

## SYSTEM DEVELOPMENT CORP SANTA MONICA CALIF

# Personal Author(s):

# Report Date:

## 1967-07-26

# Pagination or Media Count:

## 18.0

# Abstract:

Comment concerning a recent paper 1 on the confounded factorial approach to the construction of incomplete block designs indicates the desirability of considering other, less complex, construction methods. This paper is limited to the finite field approach to the generation of orthogonalized squares. Three general cases are discussed a where the number of elements, m, in a row or column of a square is a prime b where m is the power of a prime and c where m is a product of several primes or powers of primes. These three cases, of course, cover all positive integers. The construction methods are limited, however in that while the minimum number of orthogonalized squares is determined by the least prime power law i.e., s minp superscript i - 1, where s is the number of squares and p superscript i is the smallest number in the product m p superscript ip superscript jp superscript k, the maximum number of squares is not directly determinable. For instance, in cases where the least prime power is equal to 2 i.e., p superscript i 2, and, in general, numbers of the form 4k 2, it was long thought that not even orthogonal pairs of squares existed. However, although at least pairs of squares have been found for such cases using other methods, these methods are not covered here. Author

# Descriptors:

# Subject Categories:

- Operations Research
- Test Facilities, Equipment and Methods