Evaluation codes arising from symmetric polynomials
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909502940381184 |
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| author | Gatti, Barbara Korchmáros, Gábor Nagy, Gábor P. Lavorante, Vincenzo Pallozzi Schulte, Gioia |
| author_facet | Gatti, Barbara Korchmáros, Gábor Nagy, Gábor P. Lavorante, Vincenzo Pallozzi Schulte, Gioia |
| contents | Datta and Johnsen (Des. Codes and Cryptogr., {\bf{91}} (2023), 747-761) introduced a new family of evalutation codes in an affine space of dimension $\ge 2$ over a finite field $\mathbb{F}_q$ where linear combinations of elementary symmetric polynomials are evaluated on the set of all points with pairwise distinct coordinates. In this paper, we propose a generalization by taking low dimensional linear systems of symmetric polynomials. Computation for small values of $q=7,9$ shows that carefully chosen generalized Datta-Johnsen codes $\left[\frac{1}{2}q(q-1),3,d\right]$ have minimum distance $d$ equal to the optimal value minus 1. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_14414 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Evaluation codes arising from symmetric polynomials Gatti, Barbara Korchmáros, Gábor Nagy, Gábor P. Lavorante, Vincenzo Pallozzi Schulte, Gioia Algebraic Geometry Datta and Johnsen (Des. Codes and Cryptogr., {\bf{91}} (2023), 747-761) introduced a new family of evalutation codes in an affine space of dimension $\ge 2$ over a finite field $\mathbb{F}_q$ where linear combinations of elementary symmetric polynomials are evaluated on the set of all points with pairwise distinct coordinates. In this paper, we propose a generalization by taking low dimensional linear systems of symmetric polynomials. Computation for small values of $q=7,9$ shows that carefully chosen generalized Datta-Johnsen codes $\left[\frac{1}{2}q(q-1),3,d\right]$ have minimum distance $d$ equal to the optimal value minus 1. |
| title | Evaluation codes arising from symmetric polynomials |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2502.14414 |