{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T00:40:11Z","timestamp":1774485611844,"version":"3.50.1"},"reference-count":13,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["LMS J. Comput. Math."],"published-print":{"date-parts":[[2013]]},"abstract":"Abstract<\/jats:title>We exhibit seven linear codes exceeding the current best known minimum distance $d$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> for their dimension $k$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> and block length $n$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. Each code is defined over ${ \\mathbb{F} }_{8} $<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, and their invariants $[n, k, d] $<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> are given by $[49, 13, 27] $<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, $[49, 14, 26] $<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, $[49, 16, 24] $<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, $[49, 17, 23] $<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, $[49, 19, 21] $<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, $[49, 25, 16] $<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> and $[49, 26, 15] $<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. Our method includes an exhaustive search of all monomial evaluation codes generated by points in the $[0, 5] \\times [0, 5] $<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> lattice square.<\/jats:p>","DOI":"10.1112\/s1461157013000041","type":"journal-article","created":{"date-parts":[[2013,5,21]],"date-time":"2013-05-21T05:39:02Z","timestamp":1369114742000},"page":"109-117","source":"Crossref","is-referenced-by-count":11,"title":["Seven new champion linear codes"],"prefix":"10.1112","volume":"16","author":[{"given":"Gavin","family":"Brown","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander M.","family":"Kasprzyk","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2013,1,1]]},"reference":[{"key":"S1461157013000041_r1","unstructured":"1. J. E. Amaya , A. J. Harry and B. M. Vega , \u2018A systematic census of generalized toric codes over ${ \\mathbb{F} }_{4} $ , ${ \\mathbb{F} }_{5} $ and ${ \\mathbb{F} }_{16} $ \u2019, Technical report, MSRI-UP, July 2009, http:\/\/www.msri.org\/web\/msri\/scientific\/workshops\/show\/-\/event\/Wm491."},{"key":"S1461157013000041_r13","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2007.07.018"},{"key":"S1461157013000041_r8","unstructured":"8. E. Guerrini , E. Bellini and M. Sala , \u2018Some bounds on the size of codes\u2019, Preprint, 2012, arXiv:1206.6006v2 [cs.IT]."},{"key":"S1461157013000041_r12","doi-asserted-by":"publisher","DOI":"10.1007\/s00200-007-0041-1"},{"key":"S1461157013000041_r4","unstructured":"4. G. Brown and A.\u00a0M. Kasprzyk , 2005\u20132013, \u2018The graded ring database\u2019, http:\/\/grdb.lboro.ac.uk\/."},{"key":"S1461157013000041_r6","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2012.07.001"},{"key":"S1461157013000041_r11","unstructured":"11. J.\u00a0B. Little , \u2018Remarks on generalized toric codes\u2019, Preprint, 2011, arXiv:1107.4530v2 [cs.IT]."},{"key":"S1461157013000041_r9","unstructured":"9. M. Grassl , \u2018Bounds on the minimum distance of linear codes and quantum codes\u2019, 2012, http:\/\/www.codetables.de\/."},{"key":"S1461157013000041_r10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-57189-3_12"},{"key":"S1461157013000041_r5","unstructured":"5. G. Brown and A.\u00a0M. Kasprzyk , \u2018Magma routines for computing sets of lattice points up to affine equivalence\u2019, 2012, http:\/\/grdb.lboro.ac.uk\/files\/toriccodes\/distinctpoints.tar.gz."},{"key":"S1461157013000041_r2","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1996.0125"},{"key":"S1461157013000041_r7","unstructured":"7. A. Carbonara , J.\u00a0P. Murillo and A. Ortiz , \u2018A census of two dimensional toric codes over Galois fields of sizes 7, 8 and 9\u2019, Tech. report, MSRI-UP, July 2009, http:\/\/www.msri.org\/web\/msri\/scientific\/workshops\/show\/-\/event\/Wm491."},{"key":"S1461157013000041_r3","unstructured":"3. G. Brown , J. Buczy\u0144ski and A. M. Kasprzyk , \u2018Convex polytopes and polyhedra\u2019, Handbook of Magma Functions, Edition 2.17, 2011, http:\/\/magma.maths.usyd.edu.au\/."}],"container-title":["LMS Journal of Computation and Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1461157013000041","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,6]],"date-time":"2019-06-06T22:28:14Z","timestamp":1559860094000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1461157013000041\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":13,"alternative-id":["S1461157013000041"],"URL":"https:\/\/doi.org\/10.1112\/s1461157013000041","relation":{},"ISSN":["1461-1570"],"issn-type":[{"value":"1461-1570","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013]]}}}