{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:08Z","timestamp":1753893848663,"version":"3.41.2"},"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>It is known that there is no extremal singly even self-dual $[n,n\/2,d]$ code with minimal shadow for $(n,d)=(24m+2,4m+4)$, $(24m+4,4m+4)$, $(24m+6,4m+4)$, $(24m+10,4m+4)$ and $(24m+22,4m+6)$.\u00a0In this paper, we study singly even self-dual codes with minimal shadow\u00a0having minimum weight $d-2$ for these $(n,d)$. For $n=24m+2$, $24m+4$ and $24m+10$, we show that the weight enumerator of a singly even self-dual $[n,n\/2,4m+2]$ code with minimal shadow is uniquely determined\u00a0and we also show that there is no singly even self-dual $[n,n\/2,4m+2]$ code with minimal shadow for $m \\ge 155$, $m \\ge 156$ and $m \\ge 160$, respectively. We demonstrate that the weight enumerator of a singly even self-dual code with minimal shadow is not uniquely determined\u00a0for parameters $[24m+6,12m+3,4m+2]$ and $[24m+22,12m+11,4m+4]$.<\/jats:p>","DOI":"10.37236\/7155","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:41:19Z","timestamp":1578670879000},"source":"Crossref","is-referenced-by-count":1,"title":["Nonexistence of Certain Singly Even Self-Dual Codes with Minimal Shadow"],"prefix":"10.37236","volume":"25","author":[{"given":"Stefka","family":"Bouyuklieva","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Masaaki","family":"Harada","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Akihiro","family":"Munemasa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2018,1,25]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p13\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p13\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:40:54Z","timestamp":1579236054000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i1p13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1,25]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,1,12]]}},"URL":"https:\/\/doi.org\/10.37236\/7155","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,1,25]]},"article-number":"P1.13"}}