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On the structure of polynomial ideal codes and additive Reed--Solomon codes — arXiv:2610.21509

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.21509
License (as archived): CC0-1.0
Archived: 2026-10-16T10:34:37.341Z
SHA-256 of the archived text: f2a1b10412b8969f0d553a73bde19b4607a77e234c3ea6283a16d425f5b933b3
Stable URL of this page: https://metraipolis.com/documento/dc_eb7bb36d2cf9

How to cite

On the structure of polynomial ideal codes and additive Reed--Solomon codes — arXiv:2610.21509 — arXiv (en), https://arxiv.org/abs/2610.21509 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_eb7bb36d2cf9 (Metraipolis archive dc_eb7bb36d2cf9, sha256 f2a1b10412b8969f0d553a73bde19b4607a77e234c3ea6283a16d425f5b933b3)

BibTeX

@misc{dceb7bb36d2cf9,
  title = {On the structure of polynomial ideal codes and additive Reed--Solomon codes — arXiv:2610.21509},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.21509},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_eb7bb36d2cf9; sha256 f2a1b10412b8969f0d553a73bde19b4607a77e234c3ea6283a16d425f5b933b3},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.21509. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study structural properties of polynomial ideal (PI) codes and additive Reed--Solomon (aRS) codes in the folded Hamming metric (equivalently, the Hamming metric over a larger alphabet). We first determine the maximum possible length of PI codes, prove that the dual of every PI code is a generalized PI code, and deduce that PI codes are dually QMDS together with an explicit formula for their weight distribution. We then show that PI codes defined by irreducible polynomials correspond to aRS codes with pairwise nonconjugate evaluation points. For these aRS codes, the previous results on PI codes apply (duality, QMDS property and weight distribution). We show that, asymptotically, aRS codes with nonconjugate evaluation points achieve the same length as PI codes. We also compute the permutation group of such aRS codes. We also extend the family of PI codes to consider arbitrary polynomial modules (not necessarily pairwise coprime), and study when these and general aRS codes satisfy the QMDS and dually QMDS properties.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.IT, nuovi lavori del giorno).
Categorie arXiv: Information Theory (cs.IT).
Pagina del lavoro: https://arxiv.org/abs/2610.21509 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-16T08:51:02.575Z dalla pagina https://arxiv.org/list/math.IT/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).