Codes of Nodal Sextics with Many Nodes

Titelangaben

Kurz, Sascha:
Codes of Nodal Sextics with Many Nodes.
In: Catanese, Fabrizio (Hrsg.): Varieties of Nodal Surfaces, Coding Theory and Discriminants of Cubic Hypersurfaces. - Cham : Springer , 2026 . - S. 193-198 . - (Lecture Notes of the Unione Matematica Italiana ; 31 )
ISBN 978-3-032-05898-0
DOI: https://doi.org/10.1007/978-3-032-05899-7_5

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Abstract

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.