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}
Pub Date : 2026-01-20DOI: 10.1007/s10623-025-01784-9
Sebastian Petit, Geertrui Van de Voorde
{"title":"On certain blocking sets and the minimum weight of the code of generalised polygons","authors":"Sebastian Petit, Geertrui Van de Voorde","doi":"10.1007/s10623-025-01784-9","DOIUrl":"https://doi.org/10.1007/s10623-025-01784-9","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"21 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146005596","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 : 2026-01-05DOI: 10.1007/s10623-025-01760-3
Zixiang Xu, Chi Hoi Yip
Given a finite abelian group G and a subset $$Jsubset G$$J⊂G with $$0in J$$0∈J , let $$D_{G}(J,N)$$DG(J,N) be the maximum size of $$Asubset G^{N}$$A⊂GN such that the difference set $$A-A$$A-A and $$J^{N}$$JN have no non-trivial intersection. Recently, this extremal problem has been widely studied for different groups G and subsets J . In this paper, we generalize and improve the relevant results by Alon and by Hegedűs by building a bridge between this problem and cyclotomic polynomials with the help of algebraic graph theory. In particular, we construct infinitely many non-trivial families of G and J for which the current known upper bounds on $$D_{G}(J, N)$$DG(J,N) can be improved exponentially.
给定一个有限阿贝尔群G和一个子集$$Jsubset G$$ J∧G，其中$$0in J$$ 0∈J，设$$D_{G}(J,N)$$ D G （J， N）是$$Asubset G^{N}$$ a∧G N的最大值，使得差分集$$A-A$$ a - a与$$J^{N}$$ J N没有非平凡交集。近年来，这一极值问题在不同群G和子集J中得到了广泛的研究。本文利用代数图论在该问题与环阵多项式之间架起一座桥梁，推广并改进了Alon和Hegedűs的相关结果。特别地，我们构造了无限多个G和J的非平凡族，对于这些族，目前已知的$$D_{G}(J, N)$$ D G （J， N）的上界可以被指数地改进。
{"title":"Intersective sets over abelian groups","authors":"Zixiang Xu, Chi Hoi Yip","doi":"10.1007/s10623-025-01760-3","DOIUrl":"https://doi.org/10.1007/s10623-025-01760-3","url":null,"abstract":"Given a finite abelian group <jats:italic>G</jats:italic> and a subset <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$Jsubset G$$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>J</mml:mi> <mml:mo>⊂</mml:mo> <mml:mi>G</mml:mi> </mml:mrow> </mml:math> </jats:alternatives> </jats:inline-formula> with <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$0in J$$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>∈</mml:mo> <mml:mi>J</mml:mi> </mml:mrow> </mml:math> </jats:alternatives> </jats:inline-formula> , let <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$D_{G}(J,N)$$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msub> <mml:mi>D</mml:mi> <mml:mi>G</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>J</mml:mi> <mml:mo>,</mml:mo> <mml:mi>N</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> </jats:alternatives> </jats:inline-formula> be the maximum size of <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$Asubset G^{N}$$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>⊂</mml:mo> <mml:msup> <mml:mi>G</mml:mi> <mml:mi>N</mml:mi> </mml:msup> </mml:mrow> </mml:math> </jats:alternatives> </jats:inline-formula> such that the difference set <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$A-A$$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>-</mml:mo> <mml:mi>A</mml:mi> </mml:mrow> </mml:math> </jats:alternatives> </jats:inline-formula> and <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$J^{N}$$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>J</mml:mi> <mml:mi>N</mml:mi> </mml:msup> </mml:math> </jats:alternatives> </jats:inline-formula> have no non-trivial intersection. Recently, this extremal problem has been widely studied for different groups <jats:italic>G</jats:italic> and subsets <jats:italic>J</jats:italic> . In this paper, we generalize and improve the relevant results by Alon and by Hegedűs by building a bridge between this problem and cyclotomic polynomials with the help of algebraic graph theory. In particular, we construct infinitely many non-trivial families of <jats:italic>G</jats:italic> and <jats:italic>J</jats:italic> for which the current known upper bounds on <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$D_{G}(J, N)$$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msub> <mml:mi>D</mml:mi> <mml:mi>G</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>J</mml:mi> <mml:mo>,</mml:mo> <mml:mi>N</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> </jats:alternatives> </jats:inline-formula> can be improved exponentially.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"18 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145902643","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 : 2026-01-05DOI: 10.1007/s10623-025-01735-4
Shun Zhang, Tairong Shi, Senpeng Wang, Jie Guan, Mingyao Gao
{"title":"Improved preimage attacks on Ascon-XOF based on linearization technique","authors":"Shun Zhang, Tairong Shi, Senpeng Wang, Jie Guan, Mingyao Gao","doi":"10.1007/s10623-025-01735-4","DOIUrl":"https://doi.org/10.1007/s10623-025-01735-4","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"183 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145903368","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 : 2026-01-05DOI: 10.1007/s10623-025-01745-2
Andrea C. Burgess, Peter Danziger, Daniel Horsley, Muhammad Tariq Javed
{"title":"Packing designs with large block size","authors":"Andrea C. Burgess, Peter Danziger, Daniel Horsley, Muhammad Tariq Javed","doi":"10.1007/s10623-025-01745-2","DOIUrl":"https://doi.org/10.1007/s10623-025-01745-2","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"28 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145902645","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 : 2026-01-05DOI: 10.1007/s10623-025-01764-z
Mohsen Bayat, Nasrin Soltankhah
{"title":"On flag-transitive 2-designs with prime block length and projective special linear groups","authors":"Mohsen Bayat, Nasrin Soltankhah","doi":"10.1007/s10623-025-01764-z","DOIUrl":"https://doi.org/10.1007/s10623-025-01764-z","url":null,"abstract":"","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"15 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145902642","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}
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