{
  "abstract": "Let $p$ be a prime and $\\mathbb{F}_q/\\mathbb{F}_r$ a finite field extension with $q=p^m$ and $r=p^s$. For any $k\\mid q-1$, we consider $r$-ary irreducible cyclic codes (ICC) of the form $C(k,q/r) = \\{(Tr_{q/r}(γω^{ik})_{i=0}^{n-1})\\}_{γ\\in \\mathbb{F}_r}$, with $ω$ a primitive element of $\\mathbb{F}_q$ and $ n= \\tfrac{q-1}{k}$, and generalized Paley (GP) graphs $Γ(k,q) = Cay(\\mathbb{F}_q, \\{ x^k : x \\in \\mathbb{F}_q^* \\})$. We show that there is a simple closed formula relating the weight distribution of $C(k,q/r)$ with the spectrum of $Γ(k_r,q)$, where $k_r=\\gcd(k, \\frac{q-1}{r-1})$. Then, we give $Spec(Γ(k,q))$ explicitly for those graphs associated with irreducible 2-weight cyclic codes in the semiprimitive and exceptional cases. Finally, we give the weight enumerators of irreducible cyclic codes associated with Hamming GP-graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28546",
  "author_total": 2,
  "authors": [
    {
      "name": "Ricardo A. Podestá"
    },
    {
      "name": "Denis E. Videla"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/86r8m1hsjawd6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28546",
  "fulltext_url": null,
  "id": "86r8m1hsjawd6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28546",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7214300333",
  "pdf_url": "https://arxiv.org/pdf/2609.28546",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/86r8m1hsjawd6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.28546",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28546"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The spectral relation between irreducible cyclic codes and generalized Paley graphs",
  "title_text": "The spectral relation between irreducible cyclic codes and generalized Paley graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/86r8m1hsjawd6",
  "venue": "arXiv",
  "versions": []
}