Quaternion orthogonal designs from complex companion designs

Sarah Spence Adams, Jennifer Seberry, Nathaniel Karst, Jonathan Pollack, Tadeusz A. Wysocki

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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-time-polarization 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 quaternion orthogonal designs on complex variables for any even number of columns. A second related technique is applied to maximum rate complex orthogonal designs to generate an infinite family of quaternion orthogonal designs on complex variables such that the resulting designs have no zero entries. This second technique is also used to generate an infinite family of quaternion orthogonal designs defined over quaternion variables that display a regular redundancy. The proposed constructions are theoretically important because they provide the first known direct techniques for building infinite families of orthogonal designs over quaternion variables for any number of columns.

Original languageEnglish (US)
Pages (from-to)1056-1071
Number of pages16
JournalLinear Algebra and Its Applications
Issue number4
StatePublished - Feb 1 2008
Externally publishedYes


  • Complex orthogonal designs
  • Orthogonal designs
  • Quaternion orthogonal designs
  • Quaternions
  • Space-time block codes

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


Dive into the research topics of 'Quaternion orthogonal designs from complex companion designs'. Together they form a unique fingerprint.

Cite this