Pairwise orthogonal F-rectangle designs

Some Pairwise Balanced Designs

A pairwise balanced design, B(K; v), is a block design on v points, with block sizes taken from K, and with every pair of points occurring in a unique block; for a fixed K, B(K) is the set of all v for which a B(K; v) exists. A set, S, is a PBD-basis for the set, T , if T = B(S). Let Na(m) = {n : n ≡ a mod m}, and N≥m = {n : n ≥ m}; with Q the corresponding restriction of N to prime powers. Thi...

Automorphisms of pairwise combinatorial designs

iv

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...