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arXiv · 2606.18577

Factorizations of linearized polynomials and extremal curves in odd characteristic

Tetsushi Ito·Daichi Takeuchi·Takahiro Tsushima
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Abstract

We give a complete recipe for constructing extremal van der Geer--van der Vlugt curves over finite fields of odd characteristic. The input data consist of a nonzero element of the base field together with a linear subspace satisfying a certain trace condition. This construction may be viewed as an odd-characteristic analogue of the one previously obtained by the authors in characteristic two.

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Tetsushi Ito, Daichi Takeuchi, Takahiro Tsushima. 2026-06-17. Factorizations of linearized polynomials and extremal curves in odd characteristic. https://arxiv.org/abs/2606.18577

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