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<p>The Datta–Johnsen code is an evaluation code where the linear combinations of elementary symmetric polynomials are evaluated on the set of all points with pairwise distinct coordinates in an affine space of dimension <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\ge \, 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>≥</mo> <mspace width="0.166667em" /> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> over a finite field <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb {F}_q\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">F</mi> <mi>q</mi> </msub> </math></EquationSource> </InlineEquation>. A generalization is obtained by taking a low dimensional linear system of symmetric polynomials. The odd characteristic case was the subject of a recent paper. Here, the even characteristic case is investigated.</p>

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Evaluation codes from linear systems of conics

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年7月15日

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  • Barbara Gatti,
  • Gábor Korchmáros,
  • Gioia Schulte

摘要

The Datta–Johnsen code is an evaluation code where the linear combinations of elementary symmetric polynomials are evaluated on the set of all points with pairwise distinct coordinates in an affine space of dimension \(\ge \, 2\) ≥ 2 over a finite field \(\mathbb {F}_q\) F q . A generalization is obtained by taking a low dimensional linear system of symmetric polynomials. The odd characteristic case was the subject of a recent paper. Here, the even characteristic case is investigated.