{
  "annotation_id": "6a4bd2a2-8c1a-4edd-9340-fe283a0bc30c",
  "date_created": "2026-02-17T05:53:12.528000Z",
  "date_modified": "2026-02-17T05:53:12.528000Z",
  "file_hash": "1852b20cc3b8e7adfe94af9fd6d954b15bc4eab682b4f7e5847eb4834ff7be20",
  "private": false,
  "record": {
    "abstract": "Lattices and partially ordered sets have played an increasingly important role in coding theory, providing combinatorial frameworks for studying structural and algebraic properties of error-correcting codes. Motivated by recent works connecting lattice theory, anticodes, and coding-theoretic invariants, we investigate ring-linear codes endowed with the Lee metric. We introduce and characterize optimal Lee-metric anticodes over the ring $\\mathbb{Z}/p^s\\mathbb{Z}$. We show that the family of such anticodes admits a natural partition into subtypes and forms a lattice under inclusion. We establish a bijection between this lattice and a lattice of weak compositions ordered by dominance. As an application, we use this correspondence to introduce new invariants for Lee-metric codes via an anticode approach.",
    "arxiv_id": "2601.07725",
    "authors": [
      "Jessica Bariffi",
      "Drisana Bhatia",
      "Giuseppe Cotardo",
      "Violetta Weger"
    ],
    "categories": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Weak Composition Lattices and Ring-Linear Anticodes",
    "url": "https://arxiv.org/abs/2601.07725",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f4549e7b-8c8c-4cd8-9b2e-5263f10b4779",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}