On nested code pairs from the Hermitian curve

René Bødker Christensen, Olav Geil*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

2 Citations (Scopus)


Nested code pairs play a crucial role in the construction of ramp secret sharing schemes [Kurihara et al. 2012] and in the CSS construction of quantum codes [Ketkar et al. 2006]. The important parameters are (1) the codimension, (2) the relative minimum distance of the codes, and (3) the relative minimum distance of the dual set of codes. Given values for two of them, one aims at finding a set of nested codes having parameters with these values and with the remaining parameter being as large as possible. In this work we study nested codes from the Hermitian curve. For not too small codimension, we present improved constructions and provide closed formula estimates on their performance. For small codimension we show how to choose pairs of one-point algebraic geometric codes in such a way that one of the relative minimum distances is larger than the corresponding non-relative minimum distance.
Original languageEnglish
Article number101742
JournalFinite Fields and Their Applications
Number of pages26
Publication statusPublished - 2020


  • algebraic geometric codes
  • Asymmetric quantum code
  • Hermitian curve
  • ramp secret sharing
  • relative minimum distance


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