{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,26]],"date-time":"2026-01-26T19:52:45Z","timestamp":1769457165280,"version":"3.49.0"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2018,3,27]],"date-time":"2018-03-27T00:00:00Z","timestamp":1522108800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"the fundamental research funds for Heilongjiang provincial universities","award":["The study on error spreading depression in network coding"],"award-info":[{"award-number":["The study on error spreading depression in network coding"]}]},{"name":"Suihua technology office program","award":["SHKJ2015-015"],"award-info":[{"award-number":["SHKJ2015-015"]}]},{"name":"Suihua technology office program","award":["SHKJ2015-014"],"award-info":[{"award-number":["SHKJ2015-014"]}]},{"DOI":"10.13039\/501100001809","name":"National Science foundation of China","doi-asserted-by":"crossref","award":["61571150"],"award-info":[{"award-number":["61571150"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Education Office of Heilongjiang province science and technology program","award":["2016-KYYWF-0937"],"award-info":[{"award-number":["2016-KYYWF-0937"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Wireless Com Network"],"published-print":{"date-parts":[[2018,12]]},"DOI":"10.1186\/s13638-018-1076-7","type":"journal-article","created":{"date-parts":[[2018,4,4]],"date-time":"2018-04-04T04:56:58Z","timestamp":1522817818000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["The combination of sparse learning and list decoding of subspace codes for error correction in random network coding"],"prefix":"10.1186","volume":"2018","author":[{"given":"Guangzhi","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shaobin","family":"Cai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dongqiu","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wanneng","family":"Shu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunhua","family":"Ma","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mu","family":"Niu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiangnan","family":"Ding","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,3,27]]},"reference":[{"key":"1076_CR1","doi-asserted-by":"crossref","unstructured":"R Koetter, M Medard, An algebraic approach to network coding. IEEE International Symposium on Information Theory, 2001 Proceedings. 11(5), 104 (2002)","DOI":"10.1109\/TNET.2003.818197"},{"key":"1076_CR2","doi-asserted-by":"publisher","first-page":"3317","DOI":"10.1109\/TIT.2013.2243899","volume":"59","author":"V Skachek","year":"2013","unstructured":"V Skachek, O Milenkovic, A Nedi\u0107, Hybrid noncoherent network coding. IEEE Trans. Inf. Theory 59, 3317\u20133331 (2013)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1076_CR3","doi-asserted-by":"publisher","first-page":"3951","DOI":"10.1109\/TIT.2008.928291","volume":"54","author":"D Silva","year":"2008","unstructured":"D Silva, FR Kschischang, R Koetter, A rank-metric approach to error control in random network coding. Inf. Theory IEEE Trans. 54, 3951\u20133967 (2008)","journal-title":"Inf. Theory IEEE Trans."},{"key":"1076_CR4","doi-asserted-by":"publisher","first-page":"3579","DOI":"10.1109\/TIT.2008.926449","volume":"54","author":"R Koetter","year":"2007","unstructured":"R Koetter, FR Kschischang, Coding for errors and erasures in random network coding. IEEE Trans. Inf. Theory 54, 3579\u20133591 (2007)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1076_CR5","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1002\/ett.1290","volume":"19","author":"S Yang","year":"2012","unstructured":"S Yang, RW Yeung, Z Zhang, Weight properties of network codes. Eur. Trans. Telecommun. 19, 371\u2013383 (2012)","journal-title":"Eur. Trans. Telecommun."},{"key":"1076_CR6","doi-asserted-by":"publisher","unstructured":"G Zhang, S Cai, Secure error-correcting (SEC) schemes for network coding through McEliece cryptosystem. Clust. Comput., 1\u20139 (2017). https:\/\/doi.org\/10.1007\/s10586-017-1294-5","DOI":"10.1007\/s10586-017-1294-5"},{"key":"1076_CR7","doi-asserted-by":"publisher","unstructured":"G Zhang, S Cai, Universal secure error-correcting (SEC) schemes for network coding via McEliece cryptosystem based on QC-LDPC codes. Clust. Comput., 1\u201312 (2017). https:\/\/doi.org\/10.1007\/s10586-017-1354-x","DOI":"10.1007\/s10586-017-1354-x"},{"key":"1076_CR8","doi-asserted-by":"crossref","unstructured":"V Guruswami, C Wang, C Xing. Explicit List-Decodable Rank-Metric and Subspace Codes via Subspace Designs. IEEE Transac. Info. Theory. 62(5), 2707\u20132718 (2016).","DOI":"10.1109\/TIT.2016.2544347"},{"key":"1076_CR9","doi-asserted-by":"crossref","unstructured":"H Mahdavifar, A Vardy, Algebraic list-decoding on the operator channel. IEEE Int. Symp. Inf. Theory Proc. 41(3), 1193\u20131197 (2010)\u00a0","DOI":"10.1109\/ISIT.2010.5513656"},{"key":"1076_CR10","doi-asserted-by":"crossref","unstructured":"D Charles, K Jain, K Lauter, Signatures for network coding. Inf. Sci. Syst. 2006(1), 857\u2013863 (2006)","DOI":"10.1109\/CISS.2006.286587"},{"key":"1076_CR11","doi-asserted-by":"publisher","unstructured":"G Zhang, S Cai, D Zhang, The nonlinear network coding and its application in error-correcting codes. Wirel. Pers. Commun., 1\u201330 (2017) https:\/\/doi.org\/10.1007\/s11277-017-5109-z","DOI":"10.1007\/s11277-017-5109-z"},{"key":"1076_CR12","unstructured":"M Sanna, E Izquierdo, A survey of linear network coding and network error correction code constructions and algorithms. Int. J. Digital Multimedia Broadcasting. 2011,1687\u20137578 (2011).\u00a0"},{"key":"1076_CR13","doi-asserted-by":"crossref","unstructured":"E Kehdi, B Li, Null keys: limiting malicious attacks via null space properties of network coding. Proceedings IEEE INFOCOM. 1224\u20131232 (2009)","DOI":"10.1109\/INFCOM.2009.5062036"},{"key":"1076_CR14","doi-asserted-by":"crossref","unstructured":"Z Yu, Y Wei, B Ramkumar, Y Guan, An efficient signature-based scheme for securing network coding against pollution attacks. Infocom. Conf. Comput. Commun. IEEE, 1409\u20131417 (2008)","DOI":"10.1109\/INFOCOM.2008.199"},{"key":"1076_CR15","doi-asserted-by":"crossref","unstructured":"S Jaggi, M Langberg, S Katti, T Ho, D Katabi, M M\u00e9dard, et al., Resilient network coding in the presence of Byzantine adversaries. INFOCOM 2007. 26th IEEE Int. Conf. Comput. Commun. 54(6),\u00a0616\u2013624 (2007)","DOI":"10.1109\/INFCOM.2007.78"},{"key":"1076_CR16","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1109\/TIT.2007.909139","volume":"54","author":"Z Zhang","year":"2008","unstructured":"Z Zhang, Linear network error correction codes in packet networks. IEEE Trans. Inf. Theory 54, 209\u2013218 (2008)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1076_CR17","doi-asserted-by":"publisher","first-page":"1409","DOI":"10.1109\/TIT.2011.2106930","volume":"57","author":"S Yang","year":"2010","unstructured":"S Yang, RW Yeung, KN Chi, Refined coding bounds and code constructions for coherent network error correction. IEEE Trans. Inf. Theory 57, 1409\u20131424 (2010)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1076_CR18","doi-asserted-by":"crossref","unstructured":"G Xuan, FW Fu, Z Zhang, Construction of network error correction codes in packet networks. Int. Symp. Netw. Coding. 59(2), 1\u20136 (2011)","DOI":"10.1109\/ISNETCOD.2011.5979062"},{"key":"1076_CR19","first-page":"1729","volume-title":"Construction Algorithm for Network Error-Correcting Codes Attaining the Singleton Bound","author":"R Matsumoto","year":"2007","unstructured":"R Matsumoto, Construction Algorithm for Network Error-Correcting Codes Attaining the Singleton Bound (Oxford University Press, Oxford, 2007), pp. 1729\u20131735"},{"key":"1076_CR20","doi-asserted-by":"publisher","first-page":"272","DOI":"10.1049\/iet-com.2009.0224","volume":"4","author":"H Bahramgiri","year":"2010","unstructured":"H Bahramgiri, F Lahouti, Robust network coding against path failures. IET Commun. 4, 272\u2013284 (2010)","journal-title":"IET Commun."},{"key":"1076_CR21","doi-asserted-by":"crossref","unstructured":"P Sanders, S Egner, L Tolhuizen, Polynomial time algorithms for network information flow. Fifteenth ACM Symp. Parallel Algorithms Arch, 286\u2013294 (2003)","DOI":"10.1145\/777412.777464"},{"key":"1076_CR22","doi-asserted-by":"crossref","unstructured":"D Silva, FR Kschischang, Using rank-metric codes for error correction in random network coding. IEEE Int. Symp. Inf. Theory, 796\u2013800 (2007)","DOI":"10.1109\/ISIT.2007.4557322"},{"key":"1076_CR23","doi-asserted-by":"crossref","unstructured":"H Mahdavifar, A Vardy, Algebraic list-decoding of subspace codes with multiplicities. Commun. Control. Comput. 59(12), 1430\u20131437 (2011)","DOI":"10.1109\/TIT.2013.2281718"},{"key":"1076_CR24","doi-asserted-by":"crossref","unstructured":"Guruswami V, Sudan M. Improved decoding of Reed-Solomon and algebraic-geometry codes[J]. IEEE Transactions on Information Theory. 45(6):1757\u20131767 (2002).","DOI":"10.1109\/18.782097"},{"key":"1076_CR25","doi-asserted-by":"publisher","first-page":"4081","DOI":"10.1109\/TIT.2016.2570238","volume":"62","author":"U Mart\u00ednez-Pe\u00f1as","year":"2016","unstructured":"U Mart\u00ednez-Pe\u00f1as, On the similarities between generalized rank and Hamming weights and their applications to network coding. IEEE Trans. Inf. Theory 62, 4081\u20134095 (2016)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1076_CR26","doi-asserted-by":"publisher","first-page":"1996","DOI":"10.1109\/COMST.2014.2320099","volume":"16","author":"MA Alsheikh","year":"2014","unstructured":"MA Alsheikh, S Lin, D Niyato, HP Tan, Machine learning in wireless sensor networks: algorithms, strategies, and applications. IEEE Commun. Surv. Tutorials. 16, 1996\u20132018 (2014)","journal-title":"IEEE Commun. Surv. Tutorials."},{"key":"1076_CR27","doi-asserted-by":"crossref","unstructured":"N Nguyen, DL Jones, S Krishnamurthy, Netcompress: coupling network coding and compressed sensing for efficient data communication in wireless sensor networks. Signal. Proc. Syst., 356\u2013361 (2010)","DOI":"10.1109\/SIPS.2010.5624815"},{"key":"1076_CR28","doi-asserted-by":"crossref","unstructured":"S Feizi, M Medard, A power efficient sensing\/communication scheme: joint source-channel-network coding by using compressive sensing. Commun. Control. Comput., 1048\u20131054 (2011)","DOI":"10.1109\/Allerton.2011.6120283"},{"key":"1076_CR29","doi-asserted-by":"publisher","first-page":"1303","DOI":"10.1002\/dac.2763","volume":"28","author":"S Chen","year":"2015","unstructured":"S Chen, M Wu, K Wang, Z Sun, W Lu, Combining network coding and compressed sensing for error correction in wireless sensor networks. Int. J. Commun. Syst. 28, 1303\u20131315 (2015)","journal-title":"Int. J. Commun. Syst."},{"key":"1076_CR30","doi-asserted-by":"crossref","unstructured":"J Wright, Y Ma, Dense error correction via l1-minimization. IEEE Int. Conf. Acoust. Speech Signal. Proc.\u00a056(7), 3033\u20133036 (2009)","DOI":"10.1109\/ICASSP.2009.4960263"},{"key":"1076_CR31","doi-asserted-by":"publisher","first-page":"210","DOI":"10.1109\/TPAMI.2008.79","volume":"31","author":"J Wright","year":"2009","unstructured":"J Wright, AY Yang, A Ganesh, SS Sastry, Y Ma, Robust face recognition via sparse representation. IEEE Trans. Pattern Anal. Mach. Intell. 31, 210 (2009)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"1076_CR32","doi-asserted-by":"crossref","unstructured":"A Ganesh, J Wright, X Li, EJ Candes, Y Ma, Dense error correction for low-rank matrices via principal component pursuit. IEEE Int. Symp. Inf. Theory Proc. 41(3), 1513\u20131517 (2010)","DOI":"10.1109\/ISIT.2010.5513538"},{"key":"1076_CR33","doi-asserted-by":"crossref","unstructured":"C Qiu, N Vaswani, Recursive sparse recovery in large but correlated noise. Commun. Control. Comput. 752\u2013759 (2011)","DOI":"10.1109\/Allerton.2011.6120243"},{"key":"1076_CR34","doi-asserted-by":"publisher","first-page":"6718","DOI":"10.1109\/TIT.2011.2165803","volume":"57","author":"M Ali","year":"2011","unstructured":"M Ali, M Kuijper, A parametric approach to list decoding of Reed-Solomon codes using interpolation. IEEE Trans. Inf. Theory 57, 6718\u20136728 (2011)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1076_CR35","doi-asserted-by":"crossref","unstructured":"DE Bergsagel, CC Sprague, SW Ross, List decoding Reed-Solomon, algebraic-geometric, and gabidulin subcodes up to the singleton bound. ACM Symp. Theory. Comput.\u00a02(11),\u00a0843\u2013852 (2013)","DOI":"10.1145\/2488608.2488715"},{"key":"1076_CR36","doi-asserted-by":"crossref","unstructured":"V Guruswami, List Decoding of Error-Correcting Codes.\u00a0(Yanjing university press, Beijing, 2004)","DOI":"10.1007\/b104335"},{"key":"1076_CR37","doi-asserted-by":"publisher","first-page":"2934","DOI":"10.1109\/JSEN.2014.2386536","volume":"15","author":"K Eritmen","year":"2015","unstructured":"K Eritmen, M Keskinoz, Improving the performance of wireless sensor networks through optimized complex field network coding. IEEE Sensors J. 15, 2934\u20132946 (2015)","journal-title":"IEEE Sensors J."}],"container-title":["EURASIP Journal on Wireless Communications and Networking"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1186\/s13638-018-1076-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1186\/s13638-018-1076-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1186\/s13638-018-1076-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,3]],"date-time":"2025-07-03T11:59:42Z","timestamp":1751543982000},"score":1,"resource":{"primary":{"URL":"https:\/\/jwcn-eurasipjournals.springeropen.com\/articles\/10.1186\/s13638-018-1076-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,27]]},"references-count":37,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2018,12]]}},"alternative-id":["1076"],"URL":"https:\/\/doi.org\/10.1186\/s13638-018-1076-7","relation":{},"ISSN":["1687-1499"],"issn-type":[{"value":"1687-1499","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3,27]]},"assertion":[{"value":"7 November 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 March 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 March 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare that they have no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}},{"value":"Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Publisher\u2019s Note"}}],"article-number":"70"}}