Using cyclotomy to construct orthogonal designs

New D-optimal designs via cyclotomy and generalised cyclotomy

D-optimal designs are n x n ±l-matrices where n == 2 mod 4 with maximum determinant. D-optimal designs obtained via circulant matrices are equivalent to 2-{ v; kl i k2 i k1 + k2 ~(v 1)} supplementary difference sets, where v = ~. We use cyclotomy to construct D-optimal designs, where v is a prime. We give a generalisation of cyclotomy and extend the cyclotomic techniques which enables use to fi...

Generalized orthogonal designs

Quaternion orthogonal designs from complex companion designs

The success of applying generalized complex orthogonal designs as space–time block codes recently motivated the definition of quaternion orthogonal designs as potential building blocks for space–timepolarization block codes. This paper offers techniques for constructing quaternion orthogonal designs via combinations of specially chosen complex orthogonal designs. One technique is used to build ...

Amicable complex orthogonal designs

In this letter, we define amicable complex orthogonal designs (ACOD) and propose two systematic methods to construct higher-order ACOD’s from lower-order ACOD’s. Although the upper bound on the number of variables of ACOD’s is found to be the same as that of amicable orthogonal designs (AOD), we show that certain types of AOD’s that were previously shown to be non-existent or undecided, such as...

Theory of Orthogonal Designs

OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543 STRUCTURE OF GENERAL FACTORIAL DESIGNS . . . . . . . . . . . 543 SUITABLE CONFOUNDING RULES . . . . . . . . . . . . . . . . . . . . . 544 Design Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544 Block Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545 Gener...