Abstract
Several classes of near-MDS sets of \(\mathrm{PG}(3, q)\) are described. They are obtained either by considering the intersection of an elliptic quadric ovoid and a Suzuki-Tits ovoid of a symplectic polar space \(\mathcal {W}(3, q)\) or starting from the \(q+1\) points of a twisted cubic of \(\mathrm{PG}(3, q)\). As a by-product two classes of complete caps of \(\mathrm{PG}(4, q)\) of size \(2q^2-q\pm \sqrt{2q}+2\) are exhibited.
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Acknowledgements
This work was supported by the Italian National Group for Algebraic and Geometric Structures and their Applications (GNSAGA–INdAM). The authors would like to thank one of the anonymous referees for the valuable suggestions and remarks and D. Bartoli and M. Giulietti for fruitful discussions concerning elliptic curves.
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Communicated by I. Landjev.
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Ceria, M., Cossidente, A., Marino, G. et al. On near–MDS codes and caps. Des. Codes Cryptogr. 91, 1095–1110 (2023). https://doi.org/10.1007/s10623-022-01141-0
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DOI: https://doi.org/10.1007/s10623-022-01141-0