{"title":"小有限域上最优 LCD 码的几种构造","authors":"Shitao Li, Minjia Shi, Huizhou Liu","doi":"10.1007/s12095-024-00699-x","DOIUrl":null,"url":null,"abstract":"<p>Linear complementary dual (LCD) codes are linear codes which intersect their dual codes trivially, which have been of interest and extensively studied due to their practical applications in computational complexity and information protection. In this paper, we give some methods for constructing LCD codes over small finite fields by modifying some typical methods for constructing linear codes. We show that all odd-like binary Euclidean LCD codes, ternary Euclidean LCD codes and quaternary Hermitian LCD codes can be constructed using the modified methods. Our results improve the known lower bounds on the largest minimum distances of LCD codes. Furthermore, we give two counterexamples to disprove the conjecture proposed by Bouyuklieva (Des. Codes Cryptogr. <b>89</b>(11), 2445–2461 2021).</p>","PeriodicalId":10788,"journal":{"name":"Cryptography and Communications","volume":"17 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Several constructions of optimal LCD codes over small finite fields\",\"authors\":\"Shitao Li, Minjia Shi, Huizhou Liu\",\"doi\":\"10.1007/s12095-024-00699-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Linear complementary dual (LCD) codes are linear codes which intersect their dual codes trivially, which have been of interest and extensively studied due to their practical applications in computational complexity and information protection. In this paper, we give some methods for constructing LCD codes over small finite fields by modifying some typical methods for constructing linear codes. We show that all odd-like binary Euclidean LCD codes, ternary Euclidean LCD codes and quaternary Hermitian LCD codes can be constructed using the modified methods. Our results improve the known lower bounds on the largest minimum distances of LCD codes. Furthermore, we give two counterexamples to disprove the conjecture proposed by Bouyuklieva (Des. Codes Cryptogr. <b>89</b>(11), 2445–2461 2021).</p>\",\"PeriodicalId\":10788,\"journal\":{\"name\":\"Cryptography and Communications\",\"volume\":\"17 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-02-05\",\"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/s12095-024-00699-x\",\"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/s12095-024-00699-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Several constructions of optimal LCD codes over small finite fields
Linear complementary dual (LCD) codes are linear codes which intersect their dual codes trivially, which have been of interest and extensively studied due to their practical applications in computational complexity and information protection. In this paper, we give some methods for constructing LCD codes over small finite fields by modifying some typical methods for constructing linear codes. We show that all odd-like binary Euclidean LCD codes, ternary Euclidean LCD codes and quaternary Hermitian LCD codes can be constructed using the modified methods. Our results improve the known lower bounds on the largest minimum distances of LCD codes. Furthermore, we give two counterexamples to disprove the conjecture proposed by Bouyuklieva (Des. Codes Cryptogr. 89(11), 2445–2461 2021).
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