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<p>Following results and ideas due to J. Pawlina and Ş. O. Tohăneanu we consider lower bounds for the minimum distances of an evaluation code obtained evaluating all degree <i>a</i> forms (or the forms in a subspace) at the points in a finite subset <i>X</i> of a projective space. We handle some cases when there are degree <i>a</i> forms vanishing on <i>X</i>. We also consider the codes obtained evaluating <i>X</i> at the subspace defined by a zero-dimensional scheme <i>Z</i> such that <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(Z\cap X=\emptyset \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>Z</mi> <mo>∩</mo> <mi>X</mi> <mo>=</mo> <mi mathvariant="normal">∅</mi> </mrow> </math></EquationSource> </InlineEquation>. These codes arise from multiple-point codes of embedded curves.</p>

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Minimum distances of evaluation codes

  • 期刊论文

  • 发表日期：

    2026年5月17日

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  • Edoardo Ballico

摘要

Following results and ideas due to J. Pawlina and Ş. O. Tohăneanu we consider lower bounds for the minimum distances of an evaluation code obtained evaluating all degree a forms (or the forms in a subspace) at the points in a finite subset X of a projective space. We handle some cases when there are degree a forms vanishing on X. We also consider the codes obtained evaluating X at the subspace defined by a zero-dimensional scheme Z such that \(Z\cap X=\emptyset \) Z ∩ X = ∅ . These codes arise from multiple-point codes of embedded curves.