{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T12:58:51Z","timestamp":1772283531620,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>One of the most intriguing problems in $q$-analogs of designs and codes is the existence question of\u00a0an infinite family of $q$-analog of Steiner systems (spreads not included) in general,\u00a0and the existence question for the $q$-analog of the Fano plane in particular.We exhibit a completely new method to attack this problem. In the process we define\u00a0a new family of designs whose existence is implied by the\u00a0existence of $q$-Steiner systems, but could exist even if the\u00a0related $q$-Steiner systems do not exist.The method is based on a possible system obtained by puncturing\u00a0all the subspaces of the $q$-Steiner system several times.\u00a0We define \u00a0the punctured system as a new type of design and\u00a0enumerate the number of subspaces of various types that it might have.\u00a0It will be evident\u00a0that its existence does not imply the existence of the related $q$-Steiner system.\u00a0On the other hand, this type of design demonstrates how close can we get to\u00a0the related $q$-Steiner system.Necessary conditions for the existence\u00a0of such designs are presented. These necessary conditions will be also necessary conditions\u00a0for the existence of the related $q$-Steiner system.\u00a0Trivial and nontrivial direct constructions\u00a0and a nontrivial recursive construction for such designs are given.\u00a0Some of the designs have a symmetric structure, which is uniform in\u00a0the dimensions of the existing subspaces in the system. Most constructions are based\u00a0on this uniform structure of the design or its punctured designs.<\/jats:p>","DOI":"10.37236\/7106","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:34:21Z","timestamp":1578670461000},"source":"Crossref","is-referenced-by-count":5,"title":["A New Approach for Examining $q$-Steiner Systems"],"prefix":"10.37236","volume":"25","author":[{"given":"Tuvi","family":"Etzion","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,4,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i2p8\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i2p8\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:34:43Z","timestamp":1579235683000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i2p8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,4,13]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,4,13]]}},"URL":"https:\/\/doi.org\/10.37236\/7106","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,4,13]]},"article-number":"P2.8"}}