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- W4309803387 abstract "Let $mathbb F_{q^n}$ denote the finite field with $q^n$ elements. In this paper we determine the number of $mathbb F_{q^n}$-rational points of the affine Artin-Schreier curve given by $y^q-y = x(x^{q^i}-x)-lambda$ and of the Artin-Schreier hypersurface $y^q-y=sum_{j=1}^r a_jx_j(x_j^{q^{i_j}}-x_j)-lambda.$ Moreover in both cases, we show that the Weil bound is attained only in the case where the trace of $lambdainmathbb F_{q^n}$ over $mathbb F_q$ is zero. We use quadratic forms and permutation matrices to determine the number of affine rational points of these curves and hypersurfaces." @default.
- W4309803387 created "2022-11-29" @default.
- W4309803387 creator A5042637212 @default.
- W4309803387 date "2022-11-21" @default.
- W4309803387 modified "2023-09-30" @default.
- W4309803387 title "On the number of rational points of Artin-Schreier curves and hypersurfaces" @default.
- W4309803387 doi "https://doi.org/10.48550/arxiv.2211.11371" @default.
- W4309803387 hasPublicationYear "2022" @default.
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