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

Pumpluen, Susanne

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.

Citation

Pumpluen, S. (2018). Quotients of orders in algebras obtained from skew polynomials with applications to coding theory. Communications in Algebra, 46(11), 5053-5072. https://doi.org/10.1080/00927872.2018.1461882

• Journal Article Type: Article
• Acceptance Date: Mar 22, 2018
• Online Publication Date: Sep 19, 2018
• Publication Date: Sep 19, 2018
• Deposit Date: Mar 26, 2018
• Publicly Available Date: Sep 20, 2019
• Journal: Communications in Algebra
• Print ISSN: 0092-7872
• Electronic ISSN: 1532-4125
• Publisher: Taylor and Francis
• Peer Reviewed: Peer Reviewed
• Volume: 46
• Issue: 11
• Pages: 5053-5072
• DOI: https://doi.org/10.1080/00927872.2018.1461882
• Public URL: https://nottingham-repository.worktribe.com/output/921135
• Publisher URL: https://www.tandfonline.com/doi/full/10.1080/00927872.2018.1461882
• Additional Information: This is an Accepted Manuscript of an article published by Taylor & Francis in Communications in Algebra on 19.09.2018, available online: http://www.tandfonline.com/10.1080/00927872.2018.1461882
• Contract Date: Mar 26, 2018