{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T07:43:45Z","timestamp":1698219825584},"reference-count":30,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2011,1,31]],"date-time":"2011-01-31T00:00:00Z","timestamp":1296432000000},"content-version":"vor","delay-in-days":5935,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Trans Emerging Tel Tech"],"published-print":{"date-parts":[[1994,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The paper concerns the covering polynomial method of decoding cyclic codes. This is an easily\u2010implementable, robust, and low\u2010complexity decoding algorithm. The determination of the exact complexity of the algorithm is a difficult open problem. In this paper several methods for constructing minimal sets of covering polynomials are proposed for the case <jats:italic>R<\/jats:italic> &lt; 2\/\u03c4, where \u03c4 is the number of errors to be corrected. Complete closed form specifications of the minimal set are given for the case where \u03c4 is even, and a computationally efficient procedure presented for general \u03c4 is shown to be optimal in many cases (and conjectured to be globally optimal). These results are sufficient to determine the exact minimal number of covering monomials for all binary cyclic codes of length up to 127 with \u03c4 &lt; 9. Closed form specifications are available for the covering polynomial set for all such codes.<\/jats:p>","DOI":"10.1002\/ett.4460050602","type":"journal-article","created":{"date-parts":[[2011,1,31]],"date-time":"2011-01-31T13:43:14Z","timestamp":1296481394000},"page":"653-664","source":"Crossref","is-referenced-by-count":2,"title":["Decoding short binary cyclic codes via covering polynomials"],"prefix":"10.1002","volume":"5","author":[{"given":"Wonjin","family":"Sung","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"John T.","family":"Coffey","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2011,1,31]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-2174-1"},{"key":"e_1_2_1_3_2","volume-title":"Error control coding: Fundamentals and applications","author":"Lin S.","year":"1983"},{"key":"e_1_2_1_4_2","volume-title":"The theory of error\u2010correcting codes","author":"MacWilliams F. 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