How to obtain lattices from (f,σ,δ)-codes via a generalization of Construction A
We show how cyclic (f,σ,δ)-codes over finite rings canonically induce a Z-lattice in RN by using certain quotients of orders in nonassociative division algebras defined using the skew polynomial f. This construction generalizes the one using certain σ-constacyclic codes by Ducoat and Oggier, which u...
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| Format: | Article |
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Springer
2018
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| Online Access: | https://eprints.nottingham.ac.uk/46898/ |
| _version_ | 1848797422177746944 |
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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 show how cyclic (f,σ,δ)-codes over finite rings canonically induce a Z-lattice in RN by using certain quotients of orders in nonassociative division algebras defined using the skew polynomial f. This construction generalizes the one using certain σ-constacyclic codes by Ducoat and Oggier, which used quotients of orders in non-commutative associative division algebras defined by f, and can be viewed as a generalization of the classical Construction A for lattices from linear codes. It has the potential to be applied to coset coding, in particular to wire-tap coding. Previous results by Ducoat and Oggier are obtained as special cases. |
| first_indexed | 2025-11-14T20:03:37Z |
| format | Article |
| id | nottingham-46898 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:03:37Z |
| publishDate | 2018 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-468982020-05-04T19:48:11Z https://eprints.nottingham.ac.uk/46898/ How to obtain lattices from (f,σ,δ)-codes via a generalization of Construction A Pumpluen, Susanne We show how cyclic (f,σ,δ)-codes over finite rings canonically induce a Z-lattice in RN by using certain quotients of orders in nonassociative division algebras defined using the skew polynomial f. This construction generalizes the one using certain σ-constacyclic codes by Ducoat and Oggier, which used quotients of orders in non-commutative associative division algebras defined by f, and can be viewed as a generalization of the classical Construction A for lattices from linear codes. It has the potential to be applied to coset coding, in particular to wire-tap coding. Previous results by Ducoat and Oggier are obtained as special cases. Springer 2018-08-01 Article PeerReviewed Pumpluen, Susanne (2018) How to obtain lattices from (f,σ,δ)-codes via a generalization of Construction A. Applicable Algebra in Engineering, Communication and Computing, 29 (4). pp. 313-333. ISSN 1432-0622 Space-time block code linear ((f σ δ)-code; nonassociative algebra; coset coding wiretap coding; Construction A; order; skew polynomial ring https://link.springer.com/article/10.1007%2Fs00200-017-0344-9 doi:10.1007/s00200-017-0344-9 doi:10.1007/s00200-017-0344-9 |
| spellingShingle | Space-time block code linear ((f σ δ)-code; nonassociative algebra; coset coding wiretap coding; Construction A; order; skew polynomial ring Pumpluen, Susanne How to obtain lattices from (f,σ,δ)-codes via a generalization of Construction A |
| title | How to obtain lattices from (f,σ,δ)-codes via a generalization of Construction A |
| title_full | How to obtain lattices from (f,σ,δ)-codes via a generalization of Construction A |
| title_fullStr | How to obtain lattices from (f,σ,δ)-codes via a generalization of Construction A |
| title_full_unstemmed | How to obtain lattices from (f,σ,δ)-codes via a generalization of Construction A |
| title_short | How to obtain lattices from (f,σ,δ)-codes via a generalization of Construction A |
| title_sort | how to obtain lattices from (f,σ,δ)-codes via a generalization of construction a |
| topic | Space-time block code linear ((f σ δ)-code; nonassociative algebra; coset coding wiretap coding; Construction A; order; skew polynomial ring |
| url | https://eprints.nottingham.ac.uk/46898/ https://eprints.nottingham.ac.uk/46898/ https://eprints.nottingham.ac.uk/46898/ |