Please use this identifier to cite or link to this item:
https://hdl.handle.net/10356/84072
Title: | Maximal Order Codes over Number Fields | Authors: | Maire, Christian Oggier, Frédérique |
Keywords: | Asymptotically Good Codes Number Field Codes |
Issue Date: | 2017 | Source: | Maire, C., & Oggier, F. (2017). Maximal Order Codes over Number Fields. Journal of Pure and Applied Algebra, in press. | Series/Report no.: | Journal of Pure and Applied Algebra | Abstract: | 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. | URI: | https://hdl.handle.net/10356/84072 http://hdl.handle.net/10220/43584 |
ISSN: | 0022-4049 | DOI: | 10.1016/j.jpaa.2017.08.009 | Schools: | School of Physical and Mathematical Sciences | Rights: | © 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]. | Fulltext Permission: | open | Fulltext Availability: | With Fulltext |
Appears in Collections: | SPMS Journal Articles |
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Maire-Oggier-ELSE-rev.pdf | 666.38 kB | Adobe PDF | View/Open |
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