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Using a computer search the unique possible code for a sextic with 65 nodes is classified. More precisely, the known coding theoretic properties of the strict code leave three numerical candidates. Incorporating known facts about half-even sets of nodes, i.e. properties of the extended code, yields the Doro-Hall code described in Sect. 4.3 as the unique possibility. For a sextic surface with 64 nodes there remain five candidates.

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Codes of Nodal Sextics with Many Nodes

  • 章节

  • 发表日期：

    2026年

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  • Sascha Kurz

摘要

Using a computer search the unique possible code for a sextic with 65 nodes is classified. More precisely, the known coding theoretic properties of the strict code leave three numerical candidates. Incorporating known facts about half-even sets of nodes, i.e. properties of the extended code, yields the Doro-Hall code described in Sect. 4.3 as the unique possibility. For a sextic surface with 64 nodes there remain five candidates.