Marcel Fernandez, John Livieratos, Sebastià Martín
{"title":"防帧代码，可分离代码和$$B_2$$代码:边界和结构","authors":"Marcel Fernandez, John Livieratos, Sebastià Martín","doi":"10.1007/s12095-023-00682-y","DOIUrl":null,"url":null,"abstract":"Abstract In this paper, constructions of frameproof codes, separable codes, and $$B_2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>B</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> codes are obtained. For each family of codes, the Lovász Local Lemmais used to establish lower bounds for the codes. The obtained bounds match all best known bounds in the literature. Our strategy allows us to present constructions of the aforementioned codes, by using the variable framework for the Lovász Local Lemma.","PeriodicalId":10788,"journal":{"name":"Cryptography and Communications","volume":"117 25","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Frameproof codes, separable codes and $$B_2$$ codes: Bounds and constructions\",\"authors\":\"Marcel Fernandez, John Livieratos, Sebastià Martín\",\"doi\":\"10.1007/s12095-023-00682-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this paper, constructions of frameproof codes, separable codes, and $$B_2$$ <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\"> <mml:msub> <mml:mi>B</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> codes are obtained. For each family of codes, the Lovász Local Lemmais used to establish lower bounds for the codes. The obtained bounds match all best known bounds in the literature. Our strategy allows us to present constructions of the aforementioned codes, by using the variable framework for the Lovász Local Lemma.\",\"PeriodicalId\":10788,\"journal\":{\"name\":\"Cryptography and Communications\",\"volume\":\"117 25\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-11-10\",\"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/s12095-023-00682-y\",\"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/s12095-023-00682-y","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Frameproof codes, separable codes and $$B_2$$ codes: Bounds and constructions
Abstract In this paper, constructions of frameproof codes, separable codes, and $$B_2$$ B2 codes are obtained. For each family of codes, the Lovász Local Lemmais used to establish lower bounds for the codes. The obtained bounds match all best known bounds in the literature. Our strategy allows us to present constructions of the aforementioned codes, by using the variable framework for the Lovász Local Lemma.
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