{
  "abstract": "We study the $(K,N,S,M,K_c)$ distributed linearly separable computation (DLSC) setting, where a master employs $N$ workers with a per-worker computation load of $M$ to recover $K_c$ deterministic linear combinations of $K$ messages in the presence of up to $S$ stragglers. We propose a DLSC framework based on nested cyclic codes that achieves $M=\\frac{K}{N}(S+K_c)$. For sufficiently large $K$, we establish the matching converse $M\\geq\\frac{K}{N}(S+K_c)$, proving the asymptotic computation load optimality of the proposed framework. By instantiating cyclic locally recoverable codes (LRCs) as base codes in the framework, the master can recover the desired $K_c$ linear combinations by contacting fewer than $N-S$ workers under many straggler scenarios. This essentially softens the straggler threshold without increasing the computation load or communication cost. Finally, we extend the construction to reduce the per-worker communication load by a factor of $m$, while achieving an asymptotically optimal computation load of $M=\\frac{K}{N}(S+mK_c)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18184",
  "author_total": 2,
  "authors": [
    {
      "name": "Anu Mathew"
    },
    {
      "name": "M. Nikhil Krishnan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d20nqmr68f28g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18184",
  "fulltext_url": null,
  "id": "d20nqmr68f28g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18184",
  "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.IT"
    ],
    [
      "openalex",
      "1705|Advanced Data Storage Technologies"
    ]
  ],
  "openalex": "W7221795367",
  "pdf_url": "https://arxiv.org/pdf/2610.18184",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d20nqmr68f28g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:20Z",
      "native_id": "2610.18184",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18184"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Deterministic Distributed Linearly Separable Computation via Nested Cyclic Codes",
  "title_text": "Deterministic Distributed Linearly Separable Computation via Nested Cyclic Codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:20Z",
  "url": "https://research.draconitic.com/paper/d20nqmr68f28g",
  "venue": "arXiv",
  "versions": []
}