Abstract
In this note we present explicit examples of maximal and minimal curves over finite fields in odd characteristic. The curves are of Artin–Schreier type and the construction is closely related to quadratic forms from \({\mathbb {F}}_{q^n}\) to \({\mathbb {F}}_q\).
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Acknowledgements
Research of the first author partially supported by Ministry for Education, University and Research of Italy (MIUR) (Project PRIN 2012 Geometrie di Galois e strutture di incidenza-Prot. N.2012XZE22K_005) and by the Italian National Group for Algebraic and Geometric Structures and their Applications (GNSAGA-INdAM). Research of the fourth author supported by Science Foundation Ireland Grant 13/IA/1914. The authors would like to thank the anonymous reviewer for his/her useful comments.
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Bartoli, D., Quoos, L., Saygı, Z. et al. Explicit maximal and minimal curves of Artin–Schreier type from quadratic forms. AAECC 32, 507–520 (2021). https://doi.org/10.1007/s00200-019-00411-0
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DOI: https://doi.org/10.1007/s00200-019-00411-0