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Designs, Codes and Cryptography最新文献

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Cliques in Paley graphs of square order and in Peisert graphs 方阶Paley图和Peisert图中的团
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2026-04-26 DOI: 10.1007/s10623-026-01850-w
Andries E. Brouwer, Sergey Goryainov, Leonid Shalaginov, Chi Hoi Yip
{"title":"Cliques in Paley graphs of square order and in Peisert graphs","authors":"Andries E. Brouwer, Sergey Goryainov, Leonid Shalaginov, Chi Hoi Yip","doi":"10.1007/s10623-026-01850-w","DOIUrl":"https://doi.org/10.1007/s10623-026-01850-w","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147751596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
LRCS: Duality, LP bounds, and field size LRCS：对偶性、LP边界和字段大小
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2026-04-25 DOI: 10.1007/s10623-026-01829-7
Anina Gruica, Benjamin Jany, Alberto Ravagnani
{"title":"LRCS: Duality, LP bounds, and field size","authors":"Anina Gruica, Benjamin Jany, Alberto Ravagnani","doi":"10.1007/s10623-026-01829-7","DOIUrl":"https://doi.org/10.1007/s10623-026-01829-7","url":null,"abstract":"We develop a duality theory of locally recoverable codes (LRCs) and apply it to establish a series of new bounds on their parameters. We introduce and study a refined notion of weight distribution that captures the code’s locality. Using a duality result analogous to a MacWilliams identity, we then derive an LP-type bound that improves on the best known bounds in several instances. Using a dual distance bound and the theory of generalized weights, we obtain non-existence results for optimal LRCs over small fields. In particular, we show that an optimal LRC must have both minimum distance and block length relatively small compared to the field size.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"4 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147739473","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On anti-collusion codes for averaging attack in multimedia fingerprinting 多媒体指纹中平均攻击的反串通码研究
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2026-04-25 DOI: 10.1007/s10623-026-01828-8
Jing Jiang, Cailin Wen, Minquan Cheng
{"title":"On anti-collusion codes for averaging attack in multimedia fingerprinting","authors":"Jing Jiang, Cailin Wen, Minquan Cheng","doi":"10.1007/s10623-026-01828-8","DOIUrl":"https://doi.org/10.1007/s10623-026-01828-8","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"67 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147739472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Codes over an infinite family of local rings of order $$2^{5^k}$$ with two Gray maps 具有两个灰色映射的无穷一族的阶为$$2^{5^k}$$的局部环的码
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2026-04-20 DOI: 10.1007/s10623-026-01834-w
Steven T. Dougherty, Joe Gildea, Adrian Korban, Adam M. Roberts
{"title":"Codes over an infinite family of local rings of order $$2^{5^k}$$ with two Gray maps","authors":"Steven T. Dougherty, Joe Gildea, Adrian Korban, Adam M. Roberts","doi":"10.1007/s10623-026-01834-w","DOIUrl":"https://doi.org/10.1007/s10623-026-01834-w","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"28 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147733482","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Codes with symmetric distances 对称距离码
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2026-04-20 DOI: 10.1007/s10623-026-01839-5
Gábor Hegedüs, Sho Suda, Ziqing Xiang
{"title":"Codes with symmetric distances","authors":"Gábor Hegedüs, Sho Suda, Ziqing Xiang","doi":"10.1007/s10623-026-01839-5","DOIUrl":"https://doi.org/10.1007/s10623-026-01839-5","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"18 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147733483","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Self-dual matrix codes over Galois rings 伽罗瓦环上的自对偶矩阵码
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2026-04-20 DOI: 10.1007/s10623-026-01840-y
Hijiri Kawazoe, Makoto Tagami
{"title":"Self-dual matrix codes over Galois rings","authors":"Hijiri Kawazoe, Makoto Tagami","doi":"10.1007/s10623-026-01840-y","DOIUrl":"https://doi.org/10.1007/s10623-026-01840-y","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"588 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147733623","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Weights of a class of projective geometry codes 一类射影几何码的权值
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2026-04-20 DOI: 10.1007/s10623-026-01802-4
Meng Sun, Liwei Zeng, Changli Ma
{"title":"Weights of a class of projective geometry codes","authors":"Meng Sun, Liwei Zeng, Changli Ma","doi":"10.1007/s10623-026-01802-4","DOIUrl":"https://doi.org/10.1007/s10623-026-01802-4","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"57 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147733481","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New constructions of optimal symbol-pair constacyclic codes of length $$4p^s$$ 长度最优符号对恒环码的新构造 $$4p^s$$
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2026-04-20 DOI: 10.1007/s10623-026-01805-1
Amal H. Alofi, Hai Q. Dinh, Bac T. Nguyen, Nghia T. H. Tran, Hieu V. Ha
{"title":"New constructions of optimal symbol-pair constacyclic codes of length $$4p^s$$","authors":"Amal H. Alofi, Hai Q. Dinh, Bac T. Nguyen, Nghia T. H. Tran, Hieu V. Ha","doi":"10.1007/s10623-026-01805-1","DOIUrl":"https://doi.org/10.1007/s10623-026-01805-1","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"33 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147733484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A generic construction on self-orthogonal algebraic geometric codes and its applications 自正交代数几何码的一般构造及其应用
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2026-04-04 DOI: 10.1007/s10623-026-01824-y
Puyin Wang, Jinquan Luo
{"title":"A generic construction on self-orthogonal algebraic geometric codes and its applications","authors":"Puyin Wang, Jinquan Luo","doi":"10.1007/s10623-026-01824-y","DOIUrl":"https://doi.org/10.1007/s10623-026-01824-y","url":null,"abstract":"In this paper, we introduce a generalized sufficient condition for the self-orthogonality of AG codes, formulated in terms of residues and based on the algebraic structures of finite fields and the geometric properties of algebraic curves. We also present a generic construction of self-orthogonal AG codes from self-dual MDS codes. Using these approaches, we construct several families of self-dual and almost self-dual AG codes. These codes combine two merits: good performance as AG codes whose parameters are close to the Singleton bound, together with Euclidean (or Hermitian) self-dual/self-orthogonal property. Furthermore, some AG codes with Hermitian self-orthogonality can be applied to construct quantum codes with notably good parameters.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"9 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147642121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Duals of multiplicity codes 多重码的对偶
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2026-04-04 DOI: 10.1007/s10623-026-01812-2
Eduardo Camps Moreno, Adrián Fidalgo-Díaz, Hiram H. López, Umberto Martínez-Peñas, Diego Ruano, Rodrigo San-José
{"title":"Duals of multiplicity codes","authors":"Eduardo Camps Moreno, Adrián Fidalgo-Díaz, Hiram H. López, Umberto Martínez-Peñas, Diego Ruano, Rodrigo San-José","doi":"10.1007/s10623-026-01812-2","DOIUrl":"https://doi.org/10.1007/s10623-026-01812-2","url":null,"abstract":"Multivariate multiplicity codes have been recently explored because of their importance for list decoding and local decoding. Given a multivariate multiplicity code, in this paper, we compute its dimension using Gröbner basis tools, its dual in terms of indicator functions, and explicitly describe a parity-check matrix. In contrast with Reed–Muller, Reed–Solomon, univariate multiplicity, and other evaluation codes, the dual of a multivariate multiplicity code is not equivalent or isometric to a multiplicity code (i.e., this code family is not closed under duality). We use our explicit description to provide a lower bound on the minimum distance for the dual of a multiplicity code.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"7 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147642127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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