{"paper":{"title":"Rates of DNA Sequence Profiles for Practical Values of Read Lengths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Han Mao Kiah, Johan Chrisnata, Martianus Frederic Ezerman, Zuling Chang","submitted_at":"2016-07-08T09:09:08Z","abstract_excerpt":"A recent study by one of the authors has demonstrated the importance of profile vectors in DNA-based data storage. We provide exact values and lower bounds on the number of profile vectors for finite values of alphabet size $q$, read length $\\ell$, and word length $n$.Consequently, we demonstrate that for $q\\ge 2$ and $n\\le q^{\\ell/2-1}$, the number of profile vectors is at least $q^{\\kappa n}$ with $\\kappa$ very close to one.In addition to enumeration results, we provide a set of efficient encoding and decoding algorithms for each of two particular families of profile vectors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02279","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"}