Journal of Combinatorial Designs最新文献
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Lower Bounds and Construction of Detecting Arrays
检测阵列的下界与构造
IF 0.8
4区 数学
Hao Wang, Bingli Fan, Huiwen Qu
{"title":"Lower Bounds and Construction of Detecting Arrays","authors":"Hao Wang, Bingli Fan, Huiwen Qu","doi":"10.1002/jcd.70022","DOIUrl":"https://doi.org/10.1002/jcd.70022","url":null,"abstract":"<div>\u0000 \u0000 <p>Combinatorial testing has been widely used to generate test suites for detecting faults in various systems. As a type of fractional factorial design, detecting arrays have been proposed, out of the practical need for locating faults. In previous studies, the optimum detecting arrays in some cases have been determined through direct constructions and algorithmic methods. However, there are no practical lower bounds on the size of optimum detecting arrays for the general case. In this paper, we present two connections between detecting arrays and Sperner set systems that enables us to obtain lower bounds. An improved tabu search algorithm is developed for constructing mixed-level detecting arrays with a small number of rows. The performance of the algorithm is investigated by computational experiments. The experimental results show that the proposed algorithm can efficiently generate high-quality detecting arrays for different problem instances. Based on the lower bounds and algorithms presented in this study, several new optimum detecting arrays are obtained.</p>\u0000 </div>","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"34 9","pages":"415-436"},"PeriodicalIF":0.8,"publicationDate":"2026-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148533344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Quantum Latin Squares With all Possible Cardinalities
具有所有可能基数的量子拉丁方阵
IF 0.8
4区 数学
Ying Zhang, Xin Wang, Lijun Ji
{"title":"Quantum Latin Squares With all Possible Cardinalities","authors":"Ying Zhang, Xin Wang, Lijun Ji","doi":"10.1002/jcd.70021","DOIUrl":"https://doi.org/10.1002/jcd.70021","url":null,"abstract":"<div>\u0000 \u0000 <p>A quantum Latin square of order <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> (denoted as QLS<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>n</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>) is an <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>×</mo>\u0000 \u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> array whose entries are unit column vectors from the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-dimensional Hilbert space <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>ℋ</mi>\u0000 \u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, such that each row and column forms an orthonormal basis. Two unit vectors <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo></mo>\u0000 \u0000 <mrow>\u0000 <mo>∣</mo>\u0000 \u0000 <mi>u</mi>\u0000 </mrow>\u0000 \u0000 <mo>〉</mo>\u0000 </mrow>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mrow>\u0000 <mo></mo>\u0000 \u0000 <mrow>\u0000 <mo>∣</mo>\u0000 \u0000 <mi>v</mi>\u0000 </mrow>\u0000 \u0000 <mo>〉</mo>\u0000 </mrow>\u0000 \u0000 <mo>∈</mo>\u0000 \u0000 <msub>\u0000 <mi>ℋ</mi>\u0000 \u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> are regarded as identical if there exists a real number <sp","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"34 8","pages":"378-387"},"PeriodicalIF":0.8,"publicationDate":"2026-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148194017","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 the Dimension of the Space Generated by Characteristic Vectors of MRD Codes
MRD码特征向量生成空间的维数问题
IF 0.8
4区 数学
Qilong Li, Yue Zhou
{"title":"On the Dimension of the Space Generated by Characteristic Vectors of MRD Codes","authors":"Qilong Li, Yue Zhou","doi":"10.1002/jcd.70018","DOIUrl":"https://doi.org/10.1002/jcd.70018","url":null,"abstract":"<div>\u0000 \u0000 <p>Given positive integers <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>m</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msup>\u0000 <mi>m</mi>\u0000 \u0000 <mo>′</mo>\u0000 </msup>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> (<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>m</mi>\u0000 \u0000 <mo>≤</mo>\u0000 \u0000 <msup>\u0000 <mi>m</mi>\u0000 \u0000 <mo>′</mo>\u0000 </msup>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>), we call a rank-metric code <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>C</mi>\u0000 \u0000 <mo>⊆</mo>\u0000 \u0000 <msubsup>\u0000 <mi>F</mi>\u0000 \u0000 <mi>q</mi>\u0000 \u0000 <mrow>\u0000 <mi>m</mi>\u0000 \u0000 <mo>×</mo>\u0000 \u0000 <msup>\u0000 <mi>m</mi>\u0000 \u0000 <mo>′</mo>\u0000 </msup>\u0000 </mrow>\u0000 </msubsup>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, with minimum distance <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>d</mi>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mi>m</mi>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mi>t</mi>\u0000 \u0000 <mo>+</mo>\u0000 \u0000 <mn>1</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> for some <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mn>0</mn>\u0000 \u0000 <mo>≤</mo>\u0000 \u0000 <mi>t</mi>\u0000 \u0000 <mo>≤</mo>\u0000 \u0000 <mi>m</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, a maximum rank distance code (or MRD code for short) if <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"34 8","pages":"345-360"},"PeriodicalIF":0.8,"publicationDate":"2026-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148193973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Kotzig's Perfect Set Problem of Hamiltonian Cycle Decompositions of the Complete Graph
完全图哈密顿循环分解的Kotzig完美集问题
IF 0.8
4区 数学
Nobuaki Mutoh
{"title":"On Kotzig's Perfect Set Problem of Hamiltonian Cycle Decompositions of the Complete Graph","authors":"Nobuaki Mutoh","doi":"10.1002/jcd.70017","DOIUrl":"https://doi.org/10.1002/jcd.70017","url":null,"abstract":"<p>A Hamiltonian cycle decomposition (HCD) of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>K</mi>\u0000 \u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is a set of Hamiltonian cycles in which each 1-path of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>K</mi>\u0000 \u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> appears exactly once. A Dudeney set of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>K</mi>\u0000 \u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is a set of Hamiltonian cycles in which each 2-path of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>K</mi>\u0000 \u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> appears exactly once. Kotzig's perfect set of HCDs of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>K</mi>\u0000 \u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is a set of HCDs whose union forms a Dudeney set. A set of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-pairwise compatible HCDs (<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-PCH) of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>K</mi>\u0000 \u0000 <mi>n</mi>\u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"34 8","pages":"388-409"},"PeriodicalIF":0.8,"publicationDate":"2026-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jcd.70017","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148194177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Transforming Solutions for the Oberwolfach Problem into Solutions for the Spouse-Loving Variant
将Oberwolfach问题的解转化为爱配偶变体的解
IF 0.8
4区 数学
Maruša Lekše, Mateja Šajna
{"title":"Transforming Solutions for the Oberwolfach Problem into Solutions for the Spouse-Loving Variant","authors":"Maruša Lekše, Mateja Šajna","doi":"10.1002/jcd.70020","DOIUrl":"https://doi.org/10.1002/jcd.70020","url":null,"abstract":"<p>The Oberwolfach problem <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>OP</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>F</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, for a 2-factor <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>F</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>K</mi>\u0000 \u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, asks whether there exists a 2-factorization of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>K</mi>\u0000 \u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> (if <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is odd) or <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>K</mi>\u0000 \u0000 <mi>n</mi>\u0000 </msub>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mi>I</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> (if <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is even) where each 2-factor is isomorphic to <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>F</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. Here, <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"34 8","pages":"361-377"},"PeriodicalIF":0.8,"publicationDate":"2026-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jcd.70020","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148194085","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
1-Rotational Balanced Incomplete Block Designs With Block Size Four and Arbitrary Index
1-旋转平衡不完全块设计与块大小为4和任意索引
IF 0.8
4区 数学
Zian Zhang, Junling Zhou, Yanxun Chang
{"title":"1-Rotational Balanced Incomplete Block Designs With Block Size Four and Arbitrary Index","authors":"Zian Zhang, Junling Zhou, Yanxun Chang","doi":"10.1002/jcd.70013","DOIUrl":"https://doi.org/10.1002/jcd.70013","url":null,"abstract":"<div>\u0000 \u0000 <p>The necessary and sufficient conditions for the existence of 1-rotational balanced incomplete block designs with block size four and index unity have been determined to be <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>v</mi>\u0000 \u0000 <mo>≡</mo>\u0000 \u0000 <mn>4</mn>\u0000 <mspace></mspace>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>mod</mi>\u0000 <mspace></mspace>\u0000 \u0000 <mn>12</mn>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>v</mi>\u0000 \u0000 <mo>≠</mo>\u0000 \u0000 <mn>28</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> [J. Comb. Theory, Ser. A 206 (2024) 105890]. This work completely determines the existence spectrum of 1-rotational balanced incomplete block designs with block size four and any index <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>λ</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. To be specific, for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>λ</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>v</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>4</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, there exists a 1-rotational BIBD<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>v</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>4</mn>\u0000 \u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"34 7","pages":"267-290"},"PeriodicalIF":0.8,"publicationDate":"2026-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148092214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Intersection Numbers of the Natural Embedding of the Twisted Triality Hexagon T ( q 3 , q ) in PG ( 7 , q 3 )
扭曲三态六边形T （q3,）自然嵌入的交数q) in PG （7, q 3）
IF 0.8
4区 数学
Sebastian Petit, Geertrui Van de Voorde
{"title":"Intersection Numbers of the Natural Embedding of the Twisted Triality Hexagon \u0000 \u0000 \u0000 \u0000 T\u0000 \u0000 (\u0000 \u0000 \u0000 q\u0000 3\u0000 \u0000 ,\u0000 q\u0000 \u0000 )\u0000 \u0000 \u0000 \u0000 in \u0000 \u0000 \u0000 \u0000 PG\u0000 \u0000 (\u0000 \u0000 7\u0000 ,\u0000 \u0000 q\u0000 3\u0000 \u0000 \u0000 )","authors":"Sebastian Petit, Geertrui Van de Voorde","doi":"10.1002/jcd.70014","DOIUrl":"https://doi.org/10.1002/jcd.70014","url":null,"abstract":"<p>In this paper, we study and characterise the natural embedding of the twisted triality hexagon <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>T</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <msup>\u0000 <mi>q</mi>\u0000 \u0000 <mn>3</mn>\u0000 </msup>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>q</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>PG</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mn>7</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msup>\u0000 <mi>q</mi>\u0000 \u0000 <mn>3</mn>\u0000 </msup>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. We begin by describing the possible intersections of subspaces of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>PG</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mn>7</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msup>\u0000 <mi>q</mi>\u0000 \u0000 <mn>3</mn>\u0000 </msup>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>T</mi>\u0000 \u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"34 7","pages":"306-329"},"PeriodicalIF":0.8,"publicationDate":"2026-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jcd.70014","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148065779","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Construction of an Optimal ( k , n ) Multi-Receiver Authentication Code Based on Orthogonal Arrays
基于正交阵列的最优（k, n）多接收机认证码构造
IF 0.8
4区 数学
Xiuli Wang, Yangmei Deng
{"title":"Construction of an Optimal \u0000 \u0000 \u0000 \u0000 \u0000 (\u0000 \u0000 k\u0000 ,\u0000 n\u0000 \u0000 )\u0000 \u0000 \u0000 \u0000 Multi-Receiver Authentication Code Based on Orthogonal Arrays","authors":"Xiuli Wang, Yangmei Deng","doi":"10.1002/jcd.70015","DOIUrl":"https://doi.org/10.1002/jcd.70015","url":null,"abstract":"<div>\u0000 \u0000 <p>A <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>n</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> multi-receiver authentication code refers to a sender transmitting a message that needs to be authenticated to <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> receivers, so that each receiver can verify it, and any <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mn>1</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> receivers cannot deceive other receivers. In this paper, an optimal <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>n</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> multi-receiver authentication code is designed by constructing two orthogonal arrays, which satisfy that each column of one orthogonal array is friendly to the other orthogonal array. One orthogonal array with strength 2 is presented according to the mutually orthogonal Latin squares, and the other orthogonal array with strength <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is obtained by using Bush's construction. It is proved that the orthogonal array with strength <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is friendly to each column of the orthogonal array with strength 2. The probability of successful impersona","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"34 7","pages":"330-342"},"PeriodicalIF":0.8,"publicationDate":"2026-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148068130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Generalized Signed Langford Sequences
广义有符号Langford序列
IF 0.8
4区 数学
Jiwen Zhang, Haitao Cao
{"title":"Generalized Signed Langford Sequences","authors":"Jiwen Zhang, Haitao Cao","doi":"10.1002/jcd.70010","DOIUrl":"https://doi.org/10.1002/jcd.70010","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper introduces an extension of signed Langford sequences to generalized signed Langford sequences with three distinct types and investigates their existence. We establish three main existence results: (1) There exists a generalized signed Langford sequence of Type 3 except for (a) <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>d</mi>\u0000 \u0000 <mo>≡</mo>\u0000 \u0000 <mn>1</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>2</mn>\u0000 <mspace></mspace>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>mod</mi>\u0000 <mspace></mspace>\u0000 \u0000 <mn>3</mn>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>d</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>4</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>t</mi>\u0000 \u0000 <mo><</mo>\u0000 \u0000 <mn>8</mn>\u0000 \u0000 <mi>d</mi>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mn>4</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, (b) <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>d</mi>\u0000 \u0000 <mo>≡</mo>\u0000 \u0000 <mn>0</mn>\u0000 <mspace></mspace>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>mod</mi>\u0000 <mspace></mspace>\u0000 \u0000 <mn>3</mn>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>d</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>6</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"34 7","pages":"291-305"},"PeriodicalIF":0.8,"publicationDate":"2026-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148065592","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Combining the Theorems of Turán and de Bruijn–Erdős
结合Turán和de Bruijn-Erdős定理
IF 0.8
4区 数学
Sayok Chakravarty, Dhruv Mubayi
{"title":"Combining the Theorems of Turán and de Bruijn–Erdős","authors":"Sayok Chakravarty, Dhruv Mubayi","doi":"10.1002/jcd.70008","DOIUrl":"https://doi.org/10.1002/jcd.70008","url":null,"abstract":"<div>\u0000 \u0000 <p>Fix an integer <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>s</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>P</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> be a set of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> points and let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>ℒ</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> be a set of lines in a linear space such that no line in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>ℒ</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> contains more than <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>n</mi>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mn>1</mn>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>/</mo>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>s</mi>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mn>1</mn>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> points of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>P</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. Suppose that for every <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>s</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-set <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>S</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semant","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"34 6","pages":"235-258"},"PeriodicalIF":0.8,"publicationDate":"2026-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147686852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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