Maximal order codes over number fields

DOI10.1016/j.jpaa.2017.08.009zbMath1430.94101OpenAlexW2745221265MaRDI QIDQ1703597

Frédérique Oggier, Christian Maire

Publication date: 2 March 2018

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpaa.2017.08.009

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 (3)

Non-commutative ring learning with errors from cyclic algebras ⋮ List decoding of maximal order codes over number fields ⋮ Codes from unit groups of division algebras over number fields

Cites Work

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• Arithmétique des algèbres de quaternions
• Multiplicative lattices in global fields
• Tours de corps de classes et estimations de discriminants
• Tamely ramified towers and discriminant bounds for number fields. II.
• Finiteness of \(T\)-tamely ramified and \(S\)-decomposed towers and \(p\)-towers
• Construction of codes from Arakelov geometry
• Infinite class field towers of quadratic fields.
• Divisors on division algebras and error correcting codes
• A.D. Alexandrov spaces with curvature bounded below
• Constructions of codes from number fields
• Bounds for discriminants and related estimates for class numbers, regulators and zeros of zeta functions : a survey of recent results
• Effectivity of Arakelov divisors and the theta divisor of a number field

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