Codes from unit groups of division algebras over number fields

DOI10.1007/s00209-020-02614-5zbMath1491.94085arXiv1804.07108OpenAlexW3084653228MaRDI QIDQ2031713

Aurel Page, Christian Maire

Publication date: 10 June 2021

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.07108

zbMATH Keywords

asymptotically good codesdivision algebras over number fieldsnumber field codes

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) to coding theory (94B75) Quaternion and other division algebras: arithmetic, zeta functions (11R52) Arithmetic codes (94B40)

Related Items

Codes in the Sum-Rank Metric: Fundamentals and Applications

Uses Software

• PARI/GP

Cites Work

• Arithmetic subgroups of algebraic groups
• Volumes of S-arithmetic quotients of semi-simple groups. With an appendix by Moshe Jarden and Gopal Prasad
• The volume of a compact Lie group
• Tours de corps de classes et estimations de discriminants
• Tamely ramified towers and discriminant bounds for number fields. II.
• Skew and linearized Reed-Solomon codes and maximum sum rank distance codes over any division ring
• Maximal order codes over number fields
• Lie Groups
• Constructions of codes from number fields
• Eléments de Mathématique. Groupes et algèbres de Lie
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