{"paper":{"title":"Codes over rings of size four, Hermitian lattices, and corresponding theta functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"G. S. Wijesiri, T. Shaska","submitted_at":"2012-09-03T20:00:40Z","abstract_excerpt":"Let $K=Q(\\sqrt{-\\ell})$ be an imaginary quadratic field with ring of integers $\\O_K$, where $\\ell$ is a square free integer such that $\\ell\\equiv 3 \\mod 4$ and $C=[n, k]$ be a linear code defined over $\\O_K/2\\O_K$. The level $\\ell$ theta function $\\Th_{\\L_{\\ell} (C)} $ of $C$ is defined on the lattice $\\L_{\\ell} (C):= \\set {x \\in \\O_K^n : \\rho_\\ell (x) \\in C}$, where $\\rho_{\\ell}:\\O_K \\rightarrow \\O_K/2\\O_K$ is the natural projection. In this paper, we prove that: %\ni) for any $\\ell, \\ell^\\prime$ such that $\\ell \\leq \\ell^\\prime$, $\\Th_{\\Lambda_\\ell}(q)$ and $\\Th_{\\Lambda_{\\ell^\\prime}}(q)$ ha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0469","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}