Constructions for orthogonal designs using signed group orthogonal designs

Signed group orthogonal designs and their applications

Craigen introduced and studied signed group Hadamard matrices extensively in [1, 2]. Livinskyi [13], following Craigen’s lead, studied and provided a better estimate for the asymptotic existence of signed group Hadamard matrices and consequently improved the asymptotic existence of Hadamard matrices. In this paper, we introduce and study signed group orthogonal designs. The main results include...

Some constructions for amicable orthogonal designs

Hadamard matrices, orthogonal designs and amicable orthogonal designs have a number of applications in coding theory, cryptography, wireless network communication and so on. Product designs were introduced by Robinson in order to construct orthogonal designs especially full orthogonal designs (no zero entries) with maximum number of variables for some orders. He constructed product designs of o...

Some new constructions of orthogonal designs

In this paper we construct OD(4pq(q+1); pq, pq, pq, pq, pq, pq, pq, pq) for each core order q ≡ 3(mod 4), r ≥ 0 or q = 1, p odd, p ≤ 21 and p ∈ {25, 49}, and COD(2q(q + 1); q, q, q, q) for any prime power q ≡ 1(mod 4) (including q = 1), r ≥ 0.

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 ...