{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:32:13Z","timestamp":1740133933672,"version":"3.37.3"},"reference-count":18,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","funder":[{"name":"the Ph.D. Candidate Research Innovation Fund of Nankai University","award":["91822144"],"award-info":[{"award-number":["91822144"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61171082","61301137"],"award-info":[{"award-number":["61171082","61301137"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2019,8]]},"abstract":"<jats:p> In this paper, the Sphere-packing bound, Wang-Xing-Safavi-Naini bound, Johnson bound and Gilbert-Varshamov bound on the subspace code of length [Formula: see text], size [Formula: see text], minimum subspace distance [Formula: see text] based on [Formula: see text]-dimensional totally singular subspace in the [Formula: see text]-dimensional orthogonal space [Formula: see text] over finite fields [Formula: see text] of characteristic 2, denoted by [Formula: see text], are presented, where [Formula: see text] is a positive integer, [Formula: see text], [Formula: see text], [Formula: see text]. Then, we prove that [Formula: see text] codes attain the Wang-Xing-Safavi-Naini bound if and only if they are certain Steiner structures in [Formula: see text], where [Formula: see text] denotes the collection of all the [Formula: see text]-dimensional totally singular subspaces in the [Formula: see text]-dimensional orthogonal space [Formula: see text] over [Formula: see text] of characteristic 2. Finally, Gilbert-Varshamov bound and linear programming bound on the subspace code [Formula: see text] in [Formula: see text] are provided, where [Formula: see text] denotes the collection of all the totally singular subspaces in the [Formula: see text]-dimensional orthogonal space [Formula: see text] over [Formula: see text] of characteristic 2. <\/jats:p>","DOI":"10.1142\/s0129054119500199","type":"journal-article","created":{"date-parts":[[2019,8,13]],"date-time":"2019-08-13T04:24:14Z","timestamp":1565670254000},"page":"735-757","source":"Crossref","is-referenced-by-count":0,"title":["Bounds on Subspace Codes Based on Orthogonal Space Over Finite Fields of Characteristic 2"],"prefix":"10.1142","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2868-4195","authenticated-orcid":false,"given":"Gang","family":"Wang","sequence":"first","affiliation":[{"name":"Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, P. R. 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