Quotients of orders in algebras obtained from skew polynomials with applications to coding theory

Abstract

We describe families of nonassociative finite unital rings that occur as quotients of natural nonassociative orders in generalized nonassociative cyclic division algebras over number fields. These natural orders have already been used to systematically construct fully diverse fast-decodable space-time block codes. We show how the quotients of natural orders can be employed for coset coding. Previous results by Oggier and Sethuraman involving quotients of orders in associative cyclic division algebras are obtained as special cases.

The title changed from "Quotients of orders in algebras obtained from skew polynomials and possible applications" to "Quotients of orders in algebras obtained from skew polynomials with applications to coding theory". This version contains some minor corrections of the previous one, mostly typos

References in corpus (4)

• The nonassociative algebras used to build fast-decodable space-time block codes
• Finite nonassociative algebras obtained from skew polynomials and possible applications to $(f,\sigma ,\delta )$-codes
• Tensor products of nonassociative cyclic algebras
• How to obtain lattices from (f,sigma,delta)-codes via a generalization of Construction A

Cited by in corpus (1)

• How a nonassociative algebra reflects the properties of a skew polynomial