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Trace Hermitian Codes Have Vanishing Bias

Authors Swastik Kopparty , Amnon Ta-Shma , Kedem Yakirevitch

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Subject Classification

ACM Subject Classification
  • Theory of computation → Error-correcting codes
  • Mathematics of computing → Coding theory
Keywords
  • algebraic geometry codes
  • character sums
  • Stepanov method
  • error-correcting codes

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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) https://doi.org/10.4230/LIPIcs.CCC.2026.35

Author Details

Swastik Kopparty
  • Department of Mathematics and Department of Computer Science, University of Toronto, Canada
Amnon Ta-Shma
  • Department of Computer Science, Tel Aviv University, Israel
Kedem Yakirevitch
  • Department of Computer Science, Tel Aviv University, Israel

Funding

  • Kopparty, Swastik: Research supported by an NSERC Discovery Grant.
  • Ta-Shma, Amnon: Research supported by the Israel Science Foundation (grant number 443/22).
  • Yakirevitch, Kedem: Research supported by the Israel Science Foundation (grant number 443/22) and the Blavatnik fund.

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