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.

KEYWORDS:

• Coset code
• linear code
• nonassociative algebra
• skew polynomial ring space-time block code
• wiretap code

1991 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 17A35
• Secondary: 11T71
• 94B40
• 94B05