{"title":"从 2-(47,23,11) 设计衍生出长度为 48 的自双近极三元码的新实例","authors":"Sanja Rukavina , Vladimir D. Tonchev","doi":"10.1016/j.exco.2023.100130","DOIUrl":null,"url":null,"abstract":"<div><p>In a recent paper (Araya and Harada, 2023), Araya and Harada gave examples of self-dual near-extremal ternary codes of length 48 for 145 distinct values of the number <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>12</mn></mrow></msub></math></span> of codewords of minimum weight 12, and raised the question about the existence of codes for other values of <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>12</mn></mrow></msub></math></span>. In this note, we use symmetric 2-<span><math><mrow><mo>(</mo><mn>47</mn><mo>,</mo><mn>23</mn><mo>,</mo><mn>11</mn><mo>)</mo></mrow></math></span> designs with an automorphism group of order 6 to construct self-dual near-extremal ternary codes of length 48 for 150 new values of <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>12</mn></mrow></msub></math></span>.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"5 ","pages":"Article 100130"},"PeriodicalIF":0.0000,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X23000320/pdfft?md5=d212aa3ada7931c19aa8f5ca886b223c&pid=1-s2.0-S2666657X23000320-main.pdf","citationCount":"0","resultStr":"{\"title\":\"New examples of self-dual near-extremal ternary codes of length 48 derived from 2-(47,23,11) designs\",\"authors\":\"Sanja Rukavina , Vladimir D. Tonchev\",\"doi\":\"10.1016/j.exco.2023.100130\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In a recent paper (Araya and Harada, 2023), Araya and Harada gave examples of self-dual near-extremal ternary codes of length 48 for 145 distinct values of the number <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>12</mn></mrow></msub></math></span> of codewords of minimum weight 12, and raised the question about the existence of codes for other values of <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>12</mn></mrow></msub></math></span>. In this note, we use symmetric 2-<span><math><mrow><mo>(</mo><mn>47</mn><mo>,</mo><mn>23</mn><mo>,</mo><mn>11</mn><mo>)</mo></mrow></math></span> designs with an automorphism group of order 6 to construct self-dual near-extremal ternary codes of length 48 for 150 new values of <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>12</mn></mrow></msub></math></span>.</p></div>\",\"PeriodicalId\":100517,\"journal\":{\"name\":\"Examples and Counterexamples\",\"volume\":\"5 \",\"pages\":\"Article 100130\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-12-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S2666657X23000320/pdfft?md5=d212aa3ada7931c19aa8f5ca886b223c&pid=1-s2.0-S2666657X23000320-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Examples and Counterexamples\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2666657X23000320\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Examples and Counterexamples","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2666657X23000320","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
在最近的一篇论文(Araya and Harada, 2023)中,Araya和Harada给出了长度为48的自对偶近极值三进制码的例子,这些码字的最小权值为12的编号A12的145个不同值,并提出了A12的其他值是否存在码的问题。本文利用6阶自同构群的对称2-(47,23,11)设计,构造了长度为48的自对偶近极值三进制码,用于A12的150个新值。
New examples of self-dual near-extremal ternary codes of length 48 derived from 2-(47,23,11) designs
In a recent paper (Araya and Harada, 2023), Araya and Harada gave examples of self-dual near-extremal ternary codes of length 48 for 145 distinct values of the number of codewords of minimum weight 12, and raised the question about the existence of codes for other values of . In this note, we use symmetric 2- designs with an automorphism group of order 6 to construct self-dual near-extremal ternary codes of length 48 for 150 new values of .