Nonassociative algebras used to build fast-decodable space-time block
codes.
Let K/F and K/L be two cyclic Galois field extensions and
D = (K/F, σ, c) a cyclic algebra. Given an invertible element d in D, we
present three unital nonassociative algebras over the intersection of L and F
defined on the direct sum of n copies of D, employing d and the automorphism
generating the cyclic Galois group K/L to define their multiplication.
Two of these families appear either explicitly or implicitly in the designs of
fast-decodable space-time block codes in papers by Srinath, Rajan, Markin,
Oggier, and the authors.
S. Pumpluen < susanne.pumpluen@nottingham.ac.uk >
A. Steele < pmxas4@nottingham.ac.uk >