Ternary dual codes of the planes of order nine

DOI10.1016/S0378-3758(00)00290-1zbMath0978.05018OpenAlexW2034002964MaRDI QIDQ5935440

Jennifer D. Key, Marialuisa J. De Resmini

Publication date: 21 January 2002

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0378-3758(00)00290-1

zbMATH Keywords

projective planeminimum weightternary dual codes

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Combinatorial aspects of finite geometries (05B25) Other types of codes (94B60)

Related Items (4)

Embedded antipodal planes and the minimum weight of the dual code of points and lines in projective planes of order \(p^2\) ⋮ A lower bound for the minimum weight of the dual 7-ary code of a projective plane of order 49 ⋮ An upper bound for the minimum weight of the dual codes of desarguesian planes ⋮ Dual codes of translation planes

Uses Software

• Magma

Cites Work

• The \(\mathbb{F}_p\) span of the incidence matrix of a finite projective plane
• A computer search for finite projective planes of order 9
• Maximal arcs in Desarguesian planes of odd order do not exist
• Small sets of even type and codewords
• Sets of type \((m,n)\) in the affine and projective planes of order nine
• Minimum weight and dimension formulas for some geometric codes
• An easier proof of the maximal arcs conjecture
• Hyperovals in the known projective planes of order 16
• A geometric approach to a class of cyclic codes
• BCH Bounds for a Class of Cyclic Codes
• On generalized ReedMuller codes and their relatives
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