Codes from unit groups of division algebras over number fields
PAGE, Aurel
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
PAGE, Aurel
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
< Leer menos
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Idioma
en
Article de revue
Este ítem está publicado en
Mathematische Zeitschrift. 2021
Springer
Resumen en inglés
Lenstra and Guruswami described number field analogues of the algebraic geometry codes of Goppa. Recently, the first author and Oggier generalised these constructions to other arithmetic groups: unit groups in number fields ...Leer más >
Lenstra and Guruswami described number field analogues of the algebraic geometry codes of Goppa. Recently, the first author and Oggier generalised these constructions to other arithmetic groups: unit groups in number fields and orders in division algebras; they suggested to use unit groups in quaternion algebras but could not completely analyse the resulting codes. We prove that the noncommutative unit group construction yields asymptotically good families of codes for the sum-rank metric from division algebras of any degree, and we estimate the size of the alphabet in terms of the degree.< Leer menos
Palabras clave en inglés
Division Algebras over Number Fields
Asymptotically Good Codes
Number Field Codes
sum-rank metric
Proyecto ANR
Familles de fonctions L: analyse, interactions, résultats effectifs - ANR-17-CE40-0012
Ingénierie et Innovation par les sciences physiques, les savoir-faire technologiques et l'interdisciplinarité - ANR-17-EURE-0002
Ingénierie et Innovation par les sciences physiques, les savoir-faire technologiques et l'interdisciplinarité - ANR-17-EURE-0002
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