Full-diversity, high-rate space-time block codes from division algebras

By Bharat Al Sethuraman, B. Rajan, Vummintala Shashidhar. IEEE Transactions on Information Theory, 2003

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The golden code: a 2 x 2 full-rate space-time code with non-vanishing determinants (2004, methodology): “A general family of 2 × 2 full-rank and full-rate linear dispersion space-time block codes (LD-STBC) is given in [6], [7], based on cyclic division algebras.”
A unified framework for tree search decoding: rediscovering the sequential decoder (2005, background): “Interestingly, for a wide class of linear dispersion (LD) codes [12], [22]–[25], the information set is still given by , as in the simple V-BLAST case, although the generator matrix is generally not proportional to .”
Quaternion Algebras and the Algebraic Legacy of Hamilton's Quaternions (2006, methodology): “Quaternions have been used in inertial navigation systems [28], in computer graphics for computer animation [55], in image processing [49], [50], and in coding theory [ 54 ].”
Perfect Space–Time Block Codes (2006, methodology): “Proposition 1: [28] The algebraA = (K/F, σ, γ) of degreen is a division algebra if the smallest positive integert such thatγt is the norm of some element in K∗ is n.”