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]
< Reduce
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Language
en
Article de revue
This item was published in
Mathematische Zeitschrift. 2021
Springer
English Abstract
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 ...Read more >
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.Read less <
English Keywords
Division Algebras over Number Fields
Asymptotically Good Codes
Number Field Codes
sum-rank metric
ANR Project
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
Origin
Hal imported