{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T12:58:47Z","timestamp":1772283527733,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>For an $[n,k,d]_3$ code ${\\cal C}$ with $gcd(d,3)=1$, we define  a map $w_G$ from $\\Sigma={\\rm PG}(k-1,3)$ to the set of  weights of codewords of ${\\cal C}$ through a generator matrix $G$.  A $t$-flat $\\Pi$ in $\\Sigma$  is called an $(i,j)_t$ flat if $(i,j)=(|\\Pi \\cap F_0|,|\\Pi \\cap F_1|)$, where  $F_0 = \\{P \\in \\Sigma | w_G(P) \\equiv 0 \\pmod{3}\\}$,  $F_1 = \\{P \\in \\Sigma | w_G(P) \\not\\equiv 0,d \\pmod{3}\\}$.  We give geometric characterizations of $(i,j)_t$ flats, which involve  quadrics. As an application to the optimal linear codes problem, we prove  the non-existence of a $[305,6,202]_3$ code, which is a new result. <\/jats:p>","DOI":"10.37236\/98","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:36:37Z","timestamp":1578717397000},"source":"Crossref","is-referenced-by-count":4,"title":["Ternary Linear Codes and Quadrics"],"prefix":"10.37236","volume":"16","author":[{"given":"Yuri","family":"Yoshida","sequence":"first","affiliation":[]},{"given":"Tatsuya","family":"Maruta","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,1,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r9\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r9\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T03:14:29Z","timestamp":1579317269000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1,16]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/98","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1,16]]},"article-number":"R9"}}