Codes from unit groups of division algebras over number fields

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 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 division algebras of any degree, and we estimate the size of the alphabet in terms of the degree.
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Contributor : Aurel Page <>
Submitted on : Wednesday, April 18, 2018 - 11:01:20 PM
Last modification on : Monday, May 6, 2019 - 5:34:01 PM


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  • HAL Id : hal-01770396, version 1
  • ARXIV : 1804.07108


Christian Maire, Aurel Page. Codes from unit groups of division algebras over number fields. 2018. ⟨hal-01770396⟩



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