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Linear Codes over $\mathbb{F}_{q}+u\mathbb{F}_{q}$ associated with Simplicial Complexes, Their Gray Images, and Subfield Codes — arXiv:2609.11783

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.11783
License (as archived): CC0-1.0
Archived: 2026-10-16T06:20:24.000Z
SHA-256 of the archived text: 9327d83955d5ff79a02a9caee9e92405fe63c984f7b4ae6158e1c5c72ba21bfe
Stable URL of this page: https://metraipolis.com/documento/dc_bd79829a264b

How to cite

Linear Codes over $\mathbb{F}_{q}+u\mathbb{F}_{q}$ associated with Simplicial Complexes, Their Gray Images, and Subfield Codes — arXiv:2609.11783 — arXiv (en), https://arxiv.org/abs/2609.11783 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_bd79829a264b (Metraipolis archive dc_bd79829a264b, sha256 9327d83955d5ff79a02a9caee9e92405fe63c984f7b4ae6158e1c5c72ba21bfe)

BibTeX

@misc{dcbd79829a264b,
  title = {Linear Codes over $mathbbF_q+umathbbF_q$ associated with Simplicial Complexes, Their Gray Images, and Subfield Codes — arXiv:2609.11783},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.11783},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_bd79829a264b; sha256 9327d83955d5ff79a02a9caee9e92405fe63c984f7b4ae6158e1c5c72ba21bfe},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.11783. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In recent years, simplicial complexes have gained considerable attention as a useful tool for constructing distance-optimal codes over finite fields. In this article, we construct four infinite families of linear codes over the ring $\mathcal{R}=\mathbb{F}_{q}+u\mathbb{F}_{q}$ with $u^2=0$ using simplicial complexes with one or two maximal elements, and completely determine their Lee weight distributions via exponential-sum techniques. By employing a Gray map on $\mathcal{R}$, we obtain infinite families of distance-optimal codes over $\mathbb{F}_{q}$, including a near-Griesmer family, and establish sufficient conditions for their minimality. Furthermore, we investigate the corresponding subfield codes and derive sufficient conditions for their distance-optimality and minimality, yielding infinite families of Griesmer and near-Griesmer codes.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-11 in math.IT).
Categorie arXiv: Information Theory (cs.IT).
Pagina del lavoro: https://arxiv.org/abs/2609.11783 — 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 2026-10-16T06:01:23.680Z dalla pagina https://arxiv.org/catchup/math.IT/2026-09-11?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).