Quotients of orders in algebras obtained from skew polynomials with applications to coding theory
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-ti...
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| Format: | Article |
| Language: | English |
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Taylor & Francis
2018
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| Online Access: | https://eprints.nottingham.ac.uk/50667/ |
| _version_ | 1848798309690376192 |
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| author | Pumpluen, Susanne |
| author_facet | Pumpluen, Susanne |
| author_sort | Pumpluen, Susanne |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:17:44Z |
| format | Article |
| id | nottingham-50667 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:17:44Z |
| publishDate | 2018 |
| publisher | Taylor & Francis |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-506672019-09-19T04:30:14Z https://eprints.nottingham.ac.uk/50667/ Quotients of orders in algebras obtained from skew polynomials with applications to coding theory Pumpluen, Susanne 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. Taylor & Francis 2018-09-19 Article PeerReviewed application/pdf en https://eprints.nottingham.ac.uk/50667/1/QuotientsordersArxiv.pdf Pumpluen, Susanne (2018) Quotients of orders in algebras obtained from skew polynomials with applications to coding theory. Communications in Algebra, 46 (11). pp. 5053-5072. ISSN 1532-4125 https://www.tandfonline.com/doi/full/10.1080/00927872.2018.1461882 doi:10.1080/00927872.2018.1461882 doi:10.1080/00927872.2018.1461882 |
| spellingShingle | Pumpluen, Susanne Quotients of orders in algebras obtained from skew polynomials with applications to coding theory |
| title | Quotients of orders in algebras obtained from skew polynomials with applications to coding theory |
| title_full | Quotients of orders in algebras obtained from skew polynomials with applications to coding theory |
| title_fullStr | Quotients of orders in algebras obtained from skew polynomials with applications to coding theory |
| title_full_unstemmed | Quotients of orders in algebras obtained from skew polynomials with applications to coding theory |
| title_short | Quotients of orders in algebras obtained from skew polynomials with applications to coding theory |
| title_sort | quotients of orders in algebras obtained from skew polynomials with applications to coding theory |
| url | https://eprints.nottingham.ac.uk/50667/ https://eprints.nottingham.ac.uk/50667/ https://eprints.nottingham.ac.uk/50667/ |