Ken Finlayson

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.

Jacket transforms are a class of transforms that are simple to calculate, easily inverted, and size-flexible. Previously reported jacket transforms were generalizations of the well-known Walsh-Hadamard transform (WHT) and the center-weighted Hadamard transform (CWHT). In this letter, we present a new class of jacket transform not derived from either the WHT or the CWHT. This class of transform can be applied to any even length vector, is applicable to finite fields, and is useful for constructing error control codes

We introduce orthogonal designs with quaternion elements and show their existence. In future work we explore these applications to signal processing.

Jacket transforms are a class of transforms which are simple to calculate, easily inverted and are size-flexible. Previously reported jacket transforms were generalizations of the well-known Walsh-Hadamard transform (WHT) and the center-weighted Hadamard transform (CWHT). In this paper we present a new class of jacket transform not derived from either the WHT or the CWHT. This class of transform can be applied to any even length vector, and is applicable to finite fields and is useful for constructing error control codes.