{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T13:30:24Z","timestamp":1761571824440,"version":"build-2065373602"},"reference-count":31,"publisher":"Institution of Engineering and Technology (IET)","issue":"11","license":[{"start":{"date-parts":[[2020,7,1]],"date-time":"2020-07-01T00:00:00Z","timestamp":1593561600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61671391"],"award-info":[{"award-number":["61671391"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004543","name":"China Scholarship Council","doi-asserted-by":"publisher","award":["201807005013","111\u20102\u201014"],"award-info":[{"award-number":["201807005013","111\u20102\u201014"]}],"id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["ietresearch.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["IET Communications"],"published-print":{"date-parts":[[2020,7]]},"abstract":"<jats:p>\n                    The\n                    <jats:italic>r<\/jats:italic>\n                    th relative generalised Hamming weight (RGHW) of an\n                    <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/cmu2bf02517-math-0001.png\" xlink:title=\"urn:x-wiley:17518628:media:cmu2bf02517:cmu2bf02517-math-0001\"\/>\n                    linear code\n                    <jats:italic>C<\/jats:italic>\n                    and an\n                    <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/cmu2bf02517-math-0002.png\" xlink:title=\"urn:x-wiley:17518628:media:cmu2bf02517:cmu2bf02517-math-0002\"\/>\n                    subcode\n                    <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/cmu2bf02517-math-0003.png\" xlink:title=\"urn:x-wiley:17518628:media:cmu2bf02517:cmu2bf02517-math-0003\"\/>\n                    , a generalisation of generalised Hamming weight (GHW), characterises code performances of wiretap channel of type II, secure network coding, linear ramp secret sharing scheme, trellis complexity etc. In this study, the authors investigate non\u2010asymptotic and asymptotic bounds on RGHW. In the non\u2010asymptotic setting, they present a new proof of the Griesmer bound on RGHW by residue code and introduce the new concept of relative chain condition. They show that code pairs meeting the Griesmer, Singleton, and weak Plotkin bounds satisfy this condition. The notion of relative chain condition and these results provide a new perspective on researches including evaluating trellis complexity and determining the weight hierarchy of code pairs etc. In the asymptotic setting, they improve previous work by introducing two new metrics, respectively, for the cases\n                    <jats:italic>r<\/jats:italic>\n                    is fixed and\n                    <jats:italic>r<\/jats:italic>\n                    is proportionally increasing with\n                    <jats:italic>n<\/jats:italic>\n                    . They show the asymptotic Singleton, Plotkin, and Gilbert\u2013Varshamov bounds on the first metric and determine the value of the second metric, which is helpful for characterising the optimal asymptotic performances of applications and constructing the optimal coding schemes.\n                  <\/jats:p>","DOI":"10.1049\/iet-com.2019.0903","type":"journal-article","created":{"date-parts":[[2020,4,2]],"date-time":"2020-04-02T22:20:12Z","timestamp":1585866012000},"page":"1793-1803","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Bounds on relative generalised Hamming weight"],"prefix":"10.1049","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5632-2787","authenticated-orcid":false,"given":"Zhuojun","family":"Zhuang","sequence":"first","affiliation":[{"name":"Innovation Academy for Microsatellites of CAS No. 99, Haike Road Shanghai 201203 People's Republic of China"}]},{"given":"Keke","family":"Zhang","sequence":"additional","affiliation":[{"name":"Innovation Academy for Microsatellites of CAS No. 99, Haike Road Shanghai 201203 People's Republic of China"}]},{"given":"Zhen","family":"Jing","sequence":"additional","affiliation":[{"name":"Innovation Academy for Microsatellites of CAS No. 99, Haike Road Shanghai 201203 People's Republic of China"}]},{"given":"Bin","family":"Dai","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology Southwest Jiaotong University No. 111, First Section, North of Second Ring Road Chengdu Sichuan 610031 People's Republic of China"}]},{"given":"Jia","family":"Huang","sequence":"additional","affiliation":[{"name":"Innovation Academy for Microsatellites of CAS No. 99, Haike Road Shanghai 201203 People's Republic of China"}]}],"member":"265","published-online":{"date-parts":[[2020,7]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/18.133259"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1984.tb00072.x"},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(77)90078-4"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2004.842763"},{"key":"e_1_2_8_6_1","doi-asserted-by":"crossref","unstructured":"ZhangZ: \u2018Wiretap networks II with partial information leakage\u2019. 2009 Int. 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