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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.
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: [].
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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