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The Rank of the Cartier operator on Picard Curves
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abstract
For an algebraic curve $\mathcal{X}$ defined over an algebraically closed field of characteristic $p > 0$, the $a$-number $a(\mathcal{X})$ is the dimension of the space of exact holomorphic differentials on $\mathcal{X}$. We compute the $a$-number for a family of certain Picard curves, using the action of the Cartier operator on $H^0(\mathcal{X},\Omega^1)$.
Forward citations
Cited by 2 Pith papers
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Reinforcement Learning Enhanced Greedy Decoding for Quantum Stabilizer Codes over $\mathbb{F}_q$
A claimed [[27,13,4]]_3 qutrit code from separated-polynomial curves and an RL-on-Greedy decoder are presented, but internal math inconsistencies and missing simulation data undermine the claims.
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Quantum Error Correction with Goppa Codes from Maximal Curves: Design, Simulation, and Performance
The proposed quantum Goppa codes from maximal curves are not supported because the divisor degrees, dimension formulas, and parameter ranges in the paper contradict each other.
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