{"paper":{"title":"A Rate-Optimal Construction of Codes with Sequential Recovery with Low Block Length","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Balaji Srinivasan Babu, Ganesh R.Kini, P. Vijay Kumar","submitted_at":"2018-01-21T09:20:29Z","abstract_excerpt":"An erasure code is said to be a code with sequential recovery with parameters $r$ and $t$, if for any $s \\leq t$ erased code symbols, there is an $s$-step recovery process in which at each step we recover exactly one erased code symbol by contacting at most $r$ other code symbols. In earlier work by the same authors, presented at ISIT 2017, we had given a construction for binary codes with sequential recovery from $t$ erasures, with locality parameter $r$, which were optimal in terms of code rate for given $r,t$, but where the block length was large, on the order of $r^{c^t}$, for some constan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06794","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"}