Maximal order codes over number fields |
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Authors: | Christian Maire Frédérique Oggier |
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Affiliation: | 1. Laboratoire de Mathématiques de Besançon, Université Bourgogne Franche-Comté et CNRS (UMR 6623), 16 route de Gray, 25030 Besançon cédex, France;2. Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore |
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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. |
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Keywords: | 11T71 94B40 11R52 94B75 |
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