{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T05:50:54Z","timestamp":1757310654594,"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>An $(n,d)$-permutation code of size $s$ is a subset $C$ of $S_n$ with $s$ elements such that the Hamming distance $d_H$ between any two distinct elements of $C$ is at least equal to $d$. In this paper, we give new upper bounds for the maximal size $\\mu(n,d)$ of an $(n,d)$-permutation code of degree $n$ with $11\\le n\\le 14$. In order to obtain these bounds, we use the structure of association scheme of the permutation group $S_n$ and the irreducible characters of $S_n$. The upper bounds for $\\mu(n,d)$ are determined solving an optimization problem with linear inequalities.<\/jats:p>","DOI":"10.37236\/407","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:00:32Z","timestamp":1578715232000},"source":"Crossref","is-referenced-by-count":13,"title":["New Upper Bounds for the Size of Permutation Codes via Linear Programming"],"prefix":"10.37236","volume":"17","author":[{"given":"Mathieu","family":"Bogaerts","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2010,10,15]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r135\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r135\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:23:01Z","timestamp":1579303381000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1r135"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,10,15]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/407","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2010,10,15]]},"article-number":"R135"}}