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Graph-Based Linear Codes Associated with the Finite Ring $\mathbb{F}_p[x]/\langle x^4 \rangle$ — arXiv:2610.08480

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.08480
License (as archived): CC0-1.0
Archived: 2026-10-07T12:10:24.650Z
SHA-256 of the archived text: ced70a6515bf4a08a962ac5ab9e9dd05d48e9e798531cc033e82695b7d5c1e13
Stable URL of this page: https://metraipolis.com/documento/dc_fb2d4876ff92

How to cite

Graph-Based Linear Codes Associated with the Finite Ring $\mathbb{F}_p[x]/\langle x^4 \rangle$ — arXiv:2610.08480 — arXiv (en), https://arxiv.org/abs/2610.08480 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_fb2d4876ff92 (Metraipolis archive dc_fb2d4876ff92, sha256 ced70a6515bf4a08a962ac5ab9e9dd05d48e9e798531cc033e82695b7d5c1e13)

BibTeX

@misc{dcfb2d4876ff92,
  title = {Graph-Based Linear Codes Associated with the Finite Ring $mathbbF_p[x]/langle x^4 rangle$ — arXiv:2610.08480},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.08480},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_fb2d4876ff92; sha256 ced70a6515bf4a08a962ac5ab9e9dd05d48e9e798531cc033e82695b7d5c1e13},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.08480. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We investigate the linear codes derived from the zero-divisor graph $\Gamma(R)$ of the finite local ring $R = \mathbb{F}_p[x]/\langle x^4 \rangle$ for an odd prime $p$. Using an equitable partition of $Z^*(R)$, we determine the parameters of the binary incidence code of $\Gamma(R)$ and construct induced bipartite subgraph codes achieving dual minimum distance $4$. Over $\mathbb{F}_p$, we parameterize the adjacency and Laplacian codes, derive the closed-form weight distribution of the Laplacian code via the MacWilliams identity, and establish its LCD property. Additionally, we determine the automorphism groups of the graph and its matrix codes. Finally, from extremal subgraphs of $\Gamma(R)$, we construct two families of Griesmer-optimal linear codes over $\mathbb{F}_p$, comprising a constant-weight minimal code and an optimal two-weight code.

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/2610.08480 — 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 2026-10-07T11:42:17.282Z dalla pagina https://arxiv.org/list/math.IT/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).