Pub Date : 2026-01-26DOI: 10.1007/s10623-025-01777-8
Sam Adriaensen, Tamás Szőnyi, Zsuzsa Weiner
{"title":"Multisets with few special directions and small weight codewords in desarguesian planes","authors":"Sam Adriaensen, Tamás Szőnyi, Zsuzsa Weiner","doi":"10.1007/s10623-025-01777-8","DOIUrl":"https://doi.org/10.1007/s10623-025-01777-8","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"85 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146048530","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}
Pub Date : 2026-01-22DOI: 10.1007/s10623-025-01766-x
Subrata Manna
{"title":"Maximum number of points of intersection of a non-degenerate Hermitian variety and a cubic hypersurface","authors":"Subrata Manna","doi":"10.1007/s10623-025-01766-x","DOIUrl":"https://doi.org/10.1007/s10623-025-01766-x","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"7 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146048535","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}
Pub Date : 2026-01-22DOI: 10.1007/s10623-025-01751-4
Chiara Castello, Heide Gluesing-Luerssen, Olga Polverino, Ferdinando Zullo
We focus on two aspects of cyclic orbit codes: invariants under equivalence and quasi-optimality. Regarding the first aspect, we establish a connection between the cyclic orbit code generated by a subspace U of $${{mathbb {F}}}_{q^n}$$Fqn and the associated linear set $$L_{Utimes U}$$LU×U . Relating the size of the linear set to the number of fractions formed by the elements of U allows us to derive new bounds on the parameters of the cyclic orbit code. In the second part, we study a particular family of (quasi-)optimal cyclic orbit codes. With the aid of these codes we establish the existence of quasi-optimal codes in even-dimensional vector spaces over finite fields of any characteristic. Finally, for the particular code family we determine the automorphism groups in various general linear group, depending on the assumed ground field, and their orbits under the Galois group over the prime field.
重点讨论了循环轨道码的两个方面：等价不变量和拟最优性。在第一方面，我们建立了由$${{mathbb {F}}}_{q^n}$$ F q n的子空间U生成的循环轨道码与相应的线性集$$L_{Utimes U}$$ L U × U之间的联系。将线性集的大小与由U的元素形成的分数的数目相联系，使我们能够推导出循环轨道码的参数的新界限。在第二部分，我们研究了一类特殊的（拟）最优循环轨道码。借助于这些码，我们建立了偶维向量空间中任意特征域上的拟最优码的存在性。最后，对于特定的码族，我们根据假定的地面场确定了各种一般线性群中的自同构群，以及它们在素场上伽罗瓦群下的轨道。
{"title":"Quasi-optimal cyclic orbit codes","authors":"Chiara Castello, Heide Gluesing-Luerssen, Olga Polverino, Ferdinando Zullo","doi":"10.1007/s10623-025-01751-4","DOIUrl":"https://doi.org/10.1007/s10623-025-01751-4","url":null,"abstract":"We focus on two aspects of cyclic orbit codes: invariants under equivalence and quasi-optimality. Regarding the first aspect, we establish a connection between the cyclic orbit code generated by a subspace <jats:italic>U</jats:italic> of <jats:inline-formula> <jats:alternatives> <jats:tex-math>$${{mathbb {F}}}_{q^n}$$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>F</mml:mi> <mml:msup> <mml:mi>q</mml:mi> <mml:mi>n</mml:mi> </mml:msup> </mml:msub> </mml:math> </jats:alternatives> </jats:inline-formula> and the associated linear set <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$L_{Utimes U}$$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>L</mml:mi> <mml:mrow> <mml:mi>U</mml:mi> <mml:mo>×</mml:mo> <mml:mi>U</mml:mi> </mml:mrow> </mml:msub> </mml:math> </jats:alternatives> </jats:inline-formula> . Relating the size of the linear set to the number of fractions formed by the elements of <jats:italic>U</jats:italic> allows us to derive new bounds on the parameters of the cyclic orbit code. In the second part, we study a particular family of (quasi-)optimal cyclic orbit codes. With the aid of these codes we establish the existence of quasi-optimal codes in even-dimensional vector spaces over finite fields of any characteristic. Finally, for the particular code family we determine the automorphism groups in various general linear group, depending on the assumed ground field, and their orbits under the Galois group over the prime field.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146048538","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}
Pub Date : 2026-01-22DOI: 10.1007/s10623-025-01747-0
Xiumei Li, Zongxi Chen, Fei Li
{"title":"Some three-weight linear codes and their complete weight enumerators and weight hierarchies","authors":"Xiumei Li, Zongxi Chen, Fei Li","doi":"10.1007/s10623-025-01747-0","DOIUrl":"https://doi.org/10.1007/s10623-025-01747-0","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146048536","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}
Pub Date : 2026-01-22DOI: 10.1007/s10623-025-01758-x
Yun Ding, Shixin Zhu
{"title":"The weight distributions and weight hierarchies of two classes of few-weight linear codes","authors":"Yun Ding, Shixin Zhu","doi":"10.1007/s10623-025-01758-x","DOIUrl":"https://doi.org/10.1007/s10623-025-01758-x","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"291 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146048537","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}
Pub Date : 2026-01-20DOI: 10.1007/s10623-025-01798-3
Alessandro Montinaro
{"title":"On the systems of Higman","authors":"Alessandro Montinaro","doi":"10.1007/s10623-025-01798-3","DOIUrl":"https://doi.org/10.1007/s10623-025-01798-3","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"99 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146005595","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：