The Theory of Quaternion Orthogonal Designs Seberry, J.; Finlayson, K.; Adams, S.S. ...
IEEE transactions on signal processing,
2008-Jan., 2008, 2008-01-00, 20080101, Letnik:
56, Številka:
1
Journal Article
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Over the past several years, there has been a renewed interest in complex orthogonal designs for their application in space-time block coding. Motivated by the success of this application, this paper ...generalizes the definition of complex orthogonal designs by introducing orthogonal designs over the quaternion domain. This paper builds a theory of these novel quaternion orthogonal designs, offers examples, and provides several construction techniques. These theoretical results, along with the results of preliminary simulations, lay the foundation for developing applications of these designs as orthogonal space-time-polarization block codes.
Hadamard matrices have many applications in several mathematical areas due to their special form and the numerous properties that characterize them. Based on a recently developed relation between ...minors of Hadamard matrices and using tools from calculus and elementary number theory, this work highlights a direct way to investigate the conditions under which an Hadamard matrix of order n − k can or cannot be embedded in an Hadamard matrix of order n. The results obtained also provide answers to the problem of determining the values of the spectrum of the determinant function for specific orders of minors of Hadamard matrices by introducing an analytic formula.
Two-level Cretan matrices are orthogonal matrices with two elements, x and y. At least one element
per row and column is 1 and the other element has modulus ≤ 1. These have been studied in the ...Russian
literature for applications in image processing and compression. Cretan matrices have been found by both
mathematical and computational methods but this paper concentrates on mathematical solutions for the first
time.
We give, for the first time, families of Cretan matrices constructed using the incidence matrix of a symmetric
balanced incomplete block design and Hadamard related difference sets.
Complex Orthogonal Space-Time Processing in Wireless Communications incorporates orthogonal space-time processing using STBCs in MIMO wireless communication systems. Complex Orthogonal STBCs (CO ...STBCs) are given emphasis because they can be used for PSK/QAM modulation schemes and are more practical than real STBCs. The overall coverage provides general knowledge about space-time processing and its applications for broad audiences. It also includes the most up-to-date review of the literature on space-time processing in general, and space-time block processing in particular. The authors also examine open issues and problems for future research in this area.
Constitutes the refereed proceedings of the 13th Australasian Conference on Information Security and Privacy, ACISP 2008, held in Wollongong, Australia, in July 2008. This book features 33 revised ...full papers which cover a range of topics in information security, including authentication, key management, and public key cryptography.
In this paper, we present an adaptively secure identity-based broadcast encryption system featuring constant sized ciphertext in the standard model. The size of the public key and the private keys of ...our system are both linear in the maximum number of receivers. In addition, our system is fully collusion-resistant and has stateless receivers. Compared with the state-of-the-art, our scheme is well optimized for the broadcast encryption. The computational complexity of decryption of our scheme depends only on the number of receivers, not the maximum number of receivers of the system. Technically, we employ dual system encryption technique and our proposal offers adaptive security under the general subgroup decisional assumption. Our scheme demonstrates that the adaptive security of the schemes utilizing a composite order group can be proven under the general subgroup decisional assumption, while many existing systems working in a composite order group are secure under multiple subgroup decision assumptions. We note that this finding is of an independent interest, which may be useful in other scenarios.
For every prime power
q
≡
7
m
o
d
16
, there are (
q
;
a
,
b
,
c
,
d
)-partitions of
GF
(
q
), with odd integers
a
,
b
,
c
, and
d
, where
a
≡
±
1
m
o
d
8
such that
q
=
a
2
+
2
(
b
2
+
c
2
+
d
2
)
...and
d
2
=
b
2
+
2
a
c
+
2
b
d
. Many results for the existence of
4
-
{
q
2
;
q
(
q
-
1
)
2
;
q
(
q
-
2
)
}
SDS which are simple homogeneous polynomials of parameters
a
,
b
,
c
and
d
of degree at most 2 have been found. Hence, for each value of
q
, the construction of SDS becomes equivalent to building a
(
q
;
a
,
b
,
c
,
d
)
-partition. Once this is done, the verification of the construction only involves verifying simple conditions on
a
,
b
,
c
and
d
which can be done manually.
We study constructions for amicable Hadamard matrices. The family for orders
, t a positive integer, is explicitly exhibited. We also show that there are amicable Hadamard matrices of order
for any ...odd integer
. Now we have orders
,
,
,
, ...,
an odd integer, for the first time.
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