{"title":"由部分传播构建的最小线性编码","authors":"Xia Wu, Wei Lu, Xiwang Cao, Gaojun Luo","doi":"10.1007/s12095-023-00689-5","DOIUrl":null,"url":null,"abstract":"<p>Partial spreads are important in finite geometry and can be used to construct linear codes. From the results in (Des. Codes Cryptogr. <b>90</b>, 1–15, 2022) by Xia Li, Qin Yue and Deng Tang, we know that if the number of the elements in a partial spread is “big enough”, then the corresponding linear code is minimal. This paper used the sufficient condition in (IEEE Trans. Inf. Theory <b>44</b>(5), 2010–2017, 1998) to prove the minimality of such linear codes. In the present paper, we use the geometric approach to study the minimality of linear codes constructed from partial spreads in all cases.</p>","PeriodicalId":10788,"journal":{"name":"Cryptography and Communications","volume":"98 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Minimal linear codes constructed from partial spreads\",\"authors\":\"Xia Wu, Wei Lu, Xiwang Cao, Gaojun Luo\",\"doi\":\"10.1007/s12095-023-00689-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Partial spreads are important in finite geometry and can be used to construct linear codes. From the results in (Des. Codes Cryptogr. <b>90</b>, 1–15, 2022) by Xia Li, Qin Yue and Deng Tang, we know that if the number of the elements in a partial spread is “big enough”, then the corresponding linear code is minimal. This paper used the sufficient condition in (IEEE Trans. Inf. Theory <b>44</b>(5), 2010–2017, 1998) to prove the minimality of such linear codes. In the present paper, we use the geometric approach to study the minimality of linear codes constructed from partial spreads in all cases.</p>\",\"PeriodicalId\":10788,\"journal\":{\"name\":\"Cryptography and Communications\",\"volume\":\"98 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-12-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Cryptography and Communications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s12095-023-00689-5\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Cryptography and Communications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s12095-023-00689-5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Minimal linear codes constructed from partial spreads
Partial spreads are important in finite geometry and can be used to construct linear codes. From the results in (Des. Codes Cryptogr. 90, 1–15, 2022) by Xia Li, Qin Yue and Deng Tang, we know that if the number of the elements in a partial spread is “big enough”, then the corresponding linear code is minimal. This paper used the sufficient condition in (IEEE Trans. Inf. Theory 44(5), 2010–2017, 1998) to prove the minimality of such linear codes. In the present paper, we use the geometric approach to study the minimality of linear codes constructed from partial spreads in all cases.
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