{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T00:57:19Z","timestamp":1778633839759,"version":"3.51.4"},"reference-count":54,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,6,30]],"date-time":"2022-06-30T00:00:00Z","timestamp":1656547200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"NSF Division of Physics","award":["1820939"],"award-info":[{"award-number":["1820939"]}]},{"name":"NSF Division of Physics","award":["2112848"],"award-info":[{"award-number":["2112848"]}]},{"name":"ITMO Fellowship and Professorship Program","award":["1820939"],"award-info":[{"award-number":["1820939"]}]},{"name":"ITMO Fellowship and Professorship Program","award":["2112848"],"award-info":[{"award-number":["2112848"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Generalized bicycle (GB) codes is a class of quantum error-correcting codes constructed from a pair of binary circulant matrices. Unlike for other simple quantum code ans\u00e4tze, unrestricted GB codes may have linear distance scaling. In addition, low-density parity-check GB codes have a naturally overcomplete set of low-weight stabilizer generators, which is expected to improve their performance in the presence of syndrome measurement errors. For such GB codes with a given maximum generator weight w, we constructed upper distance bounds by mapping them to codes local in D\u2264w\u22121 dimensions, and lower existence bounds which give d\u2265O(n1\/2). We have also conducted an exhaustive enumeration of GB codes for certain prime circulant sizes in a family of two-qubit encoding codes with row weights 4, 6, and 8; the observed distance scaling is consistent with A(w)n1\/2+B(w), where n is the code length and A(w) is increasing with w.<\/jats:p>","DOI":"10.3390\/sym14071348","type":"journal-article","created":{"date-parts":[[2022,7,1]],"date-time":"2022-07-01T01:40:36Z","timestamp":1656639636000},"page":"1348","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Distance Bounds for Generalized Bicycle Codes"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5709-7355","authenticated-orcid":false,"given":"Renyu","family":"Wang","sequence":"first","affiliation":[{"name":"Department of Physics & Astronomy, University of California, Riverside, CA 92521, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4990-0259","authenticated-orcid":false,"given":"Leonid","family":"Pryadko","sequence":"additional","affiliation":[{"name":"Department of Physics & Astronomy, University of California, Riverside, CA 92521, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Evra, S., Kaufman, T., and Z\u00e9mor, G. 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