Maximal Order Codes over Number Fields
We present constructions of codes obtained from maximal orders over number fields. Particular cases include codes from algebraic number fields by Lenstra and Guruswami, codes from units of the ring of integers of number fields, and codes from both additive and multiplicative structures of maximal or...
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sg-ntu-dr.10356-840722023-02-28T19:41:17Z Maximal Order Codes over Number Fields Maire, Christian Oggier, Frédérique School of Physical and Mathematical Sciences Asymptotically Good Codes Number Field Codes We present constructions of codes obtained from maximal orders over number fields. Particular cases include codes from algebraic number fields by Lenstra and Guruswami, codes from units of the ring of integers of number fields, and codes from both additive and multiplicative structures of maximal orders in central simple division algebras. The parameters of interest are the code rate and the minimum Hamming distance. An asymptotic study reveals several families of asymptotically good codes. Accepted version 2017-08-15T07:25:25Z 2019-12-06T15:37:44Z 2017-08-15T07:25:25Z 2019-12-06T15:37:44Z 2017 2017 Journal Article Maire, C., & Oggier, F. (2017). Maximal Order Codes over Number Fields. Journal of Pure and Applied Algebra, in press. 0022-4049 https://hdl.handle.net/10356/84072 http://hdl.handle.net/10220/43584 10.1016/j.jpaa.2017.08.009 202093 en Journal of Pure and Applied Algebra © 2017 Elsevier. This is the author created version of a work that has been peer reviewed and accepted for publication by Journal of Pure and Applied Algebra, Elsevier. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1016/j.jpaa.2017.08.009]. 49 p. application/pdf |
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Asymptotically Good Codes Number Field Codes |
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Asymptotically Good Codes Number Field Codes Maire, Christian Oggier, Frédérique Maximal Order Codes over Number Fields |
| description |
We present constructions of codes obtained from maximal orders over number fields. Particular cases include codes from algebraic number fields by Lenstra and Guruswami, codes from units of the ring of integers of number fields, and codes from both additive and multiplicative structures of maximal orders in central simple division algebras. The parameters of interest are the code rate and the minimum Hamming distance. An asymptotic study reveals several families of asymptotically good codes. |
| author2 |
School of Physical and Mathematical Sciences |
| author_facet |
School of Physical and Mathematical Sciences Maire, Christian Oggier, Frédérique |
| format |
Article |
| author |
Maire, Christian Oggier, Frédérique |
| author_sort |
Maire, Christian |
| title |
Maximal Order Codes over Number Fields |
| title_short |
Maximal Order Codes over Number Fields |
| title_full |
Maximal Order Codes over Number Fields |
| title_fullStr |
Maximal Order Codes over Number Fields |
| title_full_unstemmed |
Maximal Order Codes over Number Fields |
| title_sort |
maximal order codes over number fields |
| publishDate |
2017 |
| url |
https://hdl.handle.net/10356/84072 http://hdl.handle.net/10220/43584 |
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1759857282163671040 |