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We combine a small field with rank-metric codes to solve this problem in this paper. With a small finite field, original errors are compressed to propagated errors, and their number is smaller than the min-cut. Rank-metric codes are introduced to correct the propagated errors, while the minimum rank distance of the rank-metric code is hardly influenced by the small field. It is the first time to correct errors more than the min-cut in network coding with our method using a small field. This new error-correcting algorithm is very useful for the environment such as a wireless sensor network where network coding can be applied.<\/jats:p>","DOI":"10.1186\/s13638-020-01733-1","type":"journal-article","created":{"date-parts":[[2020,6,5]],"date-time":"2020-06-05T14:03:10Z","timestamp":1591365790000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Research on correction algorithm of propagation error in wireless sensor network coding"],"prefix":"10.1186","volume":"2020","author":[{"given":"Dongqiu","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8641-5551","authenticated-orcid":false,"given":"Mingyong","family":"Pang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guangzhi","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dandan","family":"Huang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,6,5]]},"reference":[{"issue":"1","key":"1733_CR1","doi-asserted-by":"crossref","first-page":"19","DOI":"10.4310\/CIS.2006.v6.n1.a2","volume":"6","author":"RW Yeung","year":"2006","unstructured":"R.W. 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