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<p>In the present paper, we investigate algebraic geometric codes constructed from line bundles on abelian schemes or quadric fibrations over a curve defined over a finite field. We give lower bounds for the minimum distances of these codes using intersection theory. In our approach, the existence of certain nef line bundles on fibered varieties is essential. We discuss the relation of such line bundles and the asymptotic property of semistable vector bundles under the pull-back by iterated Frobenius morphisms.</p>

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AG codes on abelian schemes and quadric fibrations over a curve

  • 期刊论文

  • 发表日期：

    2026年7月6日

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  • Tohru Nakashima

摘要

In the present paper, we investigate algebraic geometric codes constructed from line bundles on abelian schemes or quadric fibrations over a curve defined over a finite field. We give lower bounds for the minimum distances of these codes using intersection theory. In our approach, the existence of certain nef line bundles on fibered varieties is essential. We discuss the relation of such line bundles and the asymptotic property of semistable vector bundles under the pull-back by iterated Frobenius morphisms.