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Paper   IPM / M / 17560
School of Mathematics
  Title:   List decoding of maximal order codes over number fields
  Author(s):  Hassan Khodaiemehr ( Joint with N. Abdi Kourani and M. J. Nikmehr)
  Status:   Published
  Journal: Finite Fields Appl.
  Vol.:  93
  Year:  2024
  Pages:   102311
  Supported by:  IPM
In this paper, we provide two distinct list decoding algorithms tailored for specific classes of maximal order number field codes. The first algorithm focuses on the unit codes, while the second algorithm is dedicated to the Arakelov divisor-based number field codes. These codes were originally introduced by Maire and Oggier. To achieve our decoding goals, we utilize the list decoding algorithm for general number field codes proposed by Biasse and Quintin. Our approach involves carefully calculating the required parameter B from Biasse and Quintin's algorithm, and adjusting the returned list to satisfy the desired conditions. For unit codes, we consider two cases: when the underlying number field is totally real and when it has an arbitrary signature. We separate these cases because the parameter B can be improved in the totally real scenario. Additionally, we present our list decoding algorithm for Arakelov divisor-based number field codes, focusing on number fields with arbitrary signatures.

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