{"paper":{"title":"Bounds on the Zero-Error List-Decoding Capacity of the $q/(q-1)$ Channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Jaikumar Radhakrishnan, Siddharth Bhandari","submitted_at":"2018-02-23T05:40:44Z","abstract_excerpt":"We consider the problem of determining the zero-error list-decoding capacity of the $q/(q-1)$ channel studied by Elias (1988). The $q/(q-1)$ channel has input and output alphabet consisting of $q$ symbols, say, $Q = \\{x_1,x_2,\\ldots, x_q\\}$; when the channel receives an input $x \\in Q$, it outputs a symbol other than $x$ itself. Let $n(m,q,\\ell)$ be the smallest $n$ for which there is a code $C \\subseteq Q^n$ of $m$ elements such that for every list $w_1, w_2, \\ldots, w_{\\ell+1}$ of distinct code-words from $C$, there is a coordinate $j \\in [n]$ that satisfies $\\{w_1[j], w_2[j], \\ldots, w_{\\el"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08396","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"}