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Linearized Reed\u2013Solomon codes specialize to classical Reed\u2013Solomon and Gabidulin code constructions in the Hamming and rank metrics, respectively, and they admit an efficient Welch\u2013Berlekamp decoding algorithm. Applications of these codes in distributed storage systems, network coding, and multi-antenna communication are developed. Other families of codes in the sum-rank metric, including convolutional codes and subfield subcodes are described, and recent results in the general theory of codes in the sum-rank metric are surveyed.<\/jats:p>","DOI":"10.1561\/0100000120","type":"journal-article","created":{"date-parts":[[2022,5,31]],"date-time":"2022-05-31T04:10:11Z","timestamp":1653970211000},"page":"814-1031","source":"Crossref","is-referenced-by-count":23,"title":["Codes in the Sum-Rank Metric: Fundamentals and Applications"],"prefix":"10.1108","volume":"19","author":[{"given":"Umberto","family":"Mart\u00ednez-Pe\u00f1as","sequence":"first","affiliation":[{"name":"University of Valladolid ,","place":["Spain"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohannad","family":"Shehadeh","sequence":"additional","affiliation":[{"name":"University of Toronto ,","place":["Canada"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Frank R.","family":"Kschischang","sequence":"additional","affiliation":[{"name":"University of Toronto ,","place":["Canada"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"140","published-online":{"date-parts":[[2022,5,31]]},"reference":[{"issue":"4","key":"2026032712183152900_ref001","doi-asserted-by":"publisher","first-page":"1204","DOI":"10.1109\/18.850663","article-title":"Network information flow","volume":"46","author":"Ahlswede","year":"2000","journal-title":"IEEE Trans. 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