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DOI: 10.4230/LIPIcs.CCC.2026.35

Trace Hermitian Codes Have Vanishing Bias

Authors: Swastik Kopparty, Amnon Ta-Shma, and Kedem Yakirevitch

Published in: LIPIcs, Volume 383, 41st Computational Complexity Conference (CCC 2026)

Abstract

In this work we give the first proof that Trace Hermitian codes have vanishing bias. This brings to the front the question of understanding the distance of Trace AG codes, and the fascinating possibility that in some variation they might give asymptotically good codes.

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Swastik Kopparty, Amnon Ta-Shma, and Kedem Yakirevitch. Trace Hermitian Codes Have Vanishing Bias. In 41st Computational Complexity Conference (CCC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 383, pp. 35:1-35:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kopparty_et_al:LIPIcs.CCC.2026.35,
  author =	{Kopparty, Swastik and Ta-Shma, Amnon and Yakirevitch, Kedem},
  title =	{{Trace Hermitian Codes Have Vanishing Bias}},
  booktitle =	{41st Computational Complexity Conference (CCC 2026)},
  pages =	{35:1--35:28},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-437-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{383},
  editor =	{Moshkovitz, Dana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2026.35},
  URN =		{urn:nbn:de:0030-drops-270773},
  doi =		{10.4230/LIPIcs.CCC.2026.35},
  annote =	{Keywords: algebraic geometry codes, character sums, Stepanov method, error-correcting codes}
}

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Trace Hermitian Codes Have Vanishing Bias

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