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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 $${\mathbb {F}}_{q^n}$$ F q n to $${\mathbb {F}}_q$$ F q .

Explicit maximal and minimal curves of Artin–Schreier type from quadratic forms