Curves over finite fields attain the Hallouin-Perret quadratic-extension bound exactly when all real parts of their Frobenius eigenvalues coincide, which yields new coefficient bounds and low-genus classifications.
The Maximum Number of Points on a Curve of Genus 4 over F8 is 25
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Maximal curves with respect to quadratic extensions over finite fields
Curves over finite fields attain the Hallouin-Perret quadratic-extension bound exactly when all real parts of their Frobenius eigenvalues coincide, which yields new coefficient bounds and low-genus classifications.