Journal of Combinatorial Designs最新文献

{"title":"Partition of ordered triples into uniform holey ordered designs","authors":"Yuli Tan, Junling Zhou","doi":"10.1002/jcd.21933","DOIUrl":"10.1002/jcd.21933","url":null,"abstract":"<p>A large set <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mtext>LOD</mtext>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>v</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $text{LOD}(v)$</annotation>\u0000 </semantics></math> is a partition of all ordered triples of a <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>v</mi>\u0000 </mrow>\u0000 <annotation> $v$</annotation>\u0000 </semantics></math>-set into <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>v</mi>\u0000 <mo>−</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation> $v-2$</annotation>\u0000 </semantics></math> disjoint ordered designs of order <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>v</mi>\u0000 </mrow>\u0000 <annotation> $v$</annotation>\u0000 </semantics></math>. In this paper, we generalize the large set <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mtext>LOD</mtext>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>v</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $text{LOD}(v)$</annotation>\u0000 </semantics></math> with <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>v</mi>\u0000 <mo>=</mo>\u0000 <mi>g</mi>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 <annotation> $v=gt$</annotation>\u0000 </semantics></math> to the notion of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mtext>POT</mtext>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>g</mi>\u0000 <mi>t</mi>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $text{POT}({g}^{t})$</annotation>\u0000 </semantics></math>, representing a partition of all ordered triples of a <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>g</mi>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 <annotation> $gt$</annotation>\u0000 </semantics></math>-set into disjoint uniform holely ordered designs <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mtext>HOD</mtext>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>g</mi>\u0000 <mi>t</mi>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $text{HOD}({g}^{t})$</annotation>\u0000 </semantics></math>s. We show that a <math>\u0000 <semantics","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"32 5","pages":"274-293"},"PeriodicalIF":0.7,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139946640","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}

{"title":"Geometric dual and sum-rank minimal codes","authors":"Martino Borello,&nbsp;Ferdinando Zullo","doi":"10.1002/jcd.21934","DOIUrl":"10.1002/jcd.21934","url":null,"abstract":"<p>The main purpose of this paper is to further study the structure, parameters and constructions of the recently introduced minimal codes in the sum-rank metric. These objects form a bridge between the classical minimal codes in the Hamming metric, the subject of intense research over the past three decades partly because of their cryptographic properties, and the more recent rank-metric minimal codes. We prove some bounds on their parameters, existence results, and, via a tool that we name geometric dual, we manage to construct minimal codes with few weights. A generalization of the celebrated Ashikhmin–Barg condition is proved and used to ensure the minimality of certain constructions.</p>","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"32 5","pages":"238-273"},"PeriodicalIF":0.7,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139778619","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}

{"title":"Constructing MRD codes by switching","authors":"Minjia Shi,&nbsp;Denis S. Krotov,&nbsp;Ferruh Özbudak","doi":"10.1002/jcd.21931","DOIUrl":"10.1002/jcd.21931","url":null,"abstract":"<p>Maximum rank-distance (MRD) codes are (not necessarily linear) maximum codes in the rank-distance metric space on <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 <annotation> $m$</annotation>\u0000 </semantics></math>-by-<math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation> $n$</annotation>\u0000 </semantics></math> matrices over a finite field <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>F</mi>\u0000 <mi>q</mi>\u0000 </msub>\u0000 </mrow>\u0000 <annotation> ${{mathbb{F}}}_{q}$</annotation>\u0000 </semantics></math>. They are diameter perfect and have the cardinality <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>q</mi>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mi>d</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation> ${q}^{m(n-d+1)}$</annotation>\u0000 </semantics></math> if <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 <mo>≥</mo>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation> $mge n$</annotation>\u0000 </semantics></math>. We define switching in MRD codes as the replacement of special MRD subcodes by other subcodes with the same parameters. We consider constructions of MRD codes admitting switching, such as punctured twisted Gabidulin codes and direct-product codes. Using switching, we construct a huge class of MRD codes whose cardinality grows doubly exponentially in <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 <annotation> $m$</annotation>\u0000 </semantics></math> if the other parameters (<math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>,</mo>\u0000 <mspace></mspace>\u0000 <mi>q</mi>\u0000 </mrow>\u0000 <annotation> $n,,q$</annotation>\u0000 </semantics></math>, the code distance) are fixed. Moreover, we construct MRD codes with different affine ranks and aperiodic MRD codes.</p>","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"32 5","pages":"219-237"},"PeriodicalIF":0.7,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139750860","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}

{"title":"New constructions for disjoint partial difference families and external partial difference families","authors":"Sophie Huczynska,&nbsp;Laura Johnson","doi":"10.1002/jcd.21930","DOIUrl":"https://doi.org/10.1002/jcd.21930","url":null,"abstract":"<p>Recently, new combinatorial structures called disjoint partial difference families (DPDFs) and external partial difference families (EPDFs) were introduced, which simultaneously generalize partial difference sets, disjoint difference families and external difference families, and have applications in information security. So far, all known construction methods have used cyclotomy in finite fields. We present the first noncyclotomic infinite families of DPDFs which are also EPDFs, in structures other than finite fields (in particular cyclic groups and nonabelian groups). As well as direct constructions, we present an approach to constructing DPDFs/EPDFs using relative difference sets (RDSs); as part of this, we demonstrate how the well-known RDS result of Bose extends to a very natural construction for DPDFs and EPDFs.</p>","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"32 4","pages":"190-213"},"PeriodicalIF":0.7,"publicationDate":"2024-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jcd.21930","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139727696","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}

{"title":"Sailing league problems","authors":"Robert Schüler,&nbsp;Achill Schürmann","doi":"10.1002/jcd.21929","DOIUrl":"10.1002/jcd.21929","url":null,"abstract":"<p>We describe a class of combinatorial design problems which typically occur in professional sailing league competitions. We discuss connections to resolvable block designs and equitable coverings and to scheduling problems in operations research. We in particular give suitable boolean quadratic and integer linear optimization problem formulations, as well as further heuristics and restrictions, that can be used to solve sailing league problems in practice. We apply those techniques to three case studies obtained from real sailing leagues and compare the results with previously used tournament plans.</p>","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"32 4","pages":"171-189"},"PeriodicalIF":0.7,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139518112","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}

{"title":"Sporadic simple groups as flag-transitive automorphism groups of symmetric designs","authors":"Seyed Hassan Alavi,&nbsp;Ashraf Daneshkhah","doi":"10.1002/jcd.21928","DOIUrl":"10.1002/jcd.21928","url":null,"abstract":"<p>In this article, we study symmetric designs admitting flag-transitive, point-imprimitive almost simple automorphism groups with socle sporadic simple groups. As a corollary, we present a classification of symmetric designs admitting flag-transitive automorphism group whose socle is a sporadic simple group, and in conclusion, there are exactly seven such designs, one of which admits a point-imprimitive automorphism group and the remaining are point-primitive.</p>","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"32 3","pages":"127-168"},"PeriodicalIF":0.7,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138826142","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}

{"title":"Reduction for flag-transitive point-primitive 2-(v, k, λ) designs with λ prime","authors":"Yongli Zhang,&nbsp;Jianfu Chen","doi":"10.1002/jcd.21927","DOIUrl":"10.1002/jcd.21927","url":null,"abstract":"<p>It is shown that the flag-transitive, point-primitive automorphism groups of 2-<math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>v</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>k</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>λ</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation> $(v,k,lambda )$</annotation>\u0000 </semantics></math> designs with <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 </mrow>\u0000 <annotation> $lambda $</annotation>\u0000 </semantics></math> prime must be of affine type or almost simple type.</p>","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"32 2","pages":"88-101"},"PeriodicalIF":0.7,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508717","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}

{"title":"Incidence-free sets and edge domination in incidence graphs","authors":"Sam Spiro,&nbsp;Sam Adriaensen,&nbsp;Sam Mattheus","doi":"10.1002/jcd.21925","DOIUrl":"10.1002/jcd.21925","url":null,"abstract":"&lt;p&gt;A set of edges &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Γ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; ${rm{Gamma }}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of a graph &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; $G$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is an edge dominating set if every edge of &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; $G$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; intersects at least one edge of &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Γ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; ${rm{Gamma }}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, and the edge domination number &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;γ&lt;/mi&gt;\u0000 \u0000 &lt;mi&gt;e&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 \u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; ${gamma }_{e}(G)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is the smallest size of an edge dominating set. Expanding on work of Laskar and Wallis, we study &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;γ&lt;/mi&gt;\u0000 \u0000 &lt;mi&gt;e&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 \u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; ${gamma }_{e}(G)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; for graphs &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; $G$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; which are the incidence graph of some incidence structure &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; $D$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, with an emphasis on the case when &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; $D$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a symmetric design. In particular, we show in this latter case that determining &lt;math&gt;\u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"32 2","pages":"55-87"},"PeriodicalIF":0.7,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jcd.21925","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508716","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}

{"title":"On symmetric designs with flag-transitive and point-quasiprimitive automorphism groups","authors":"Zhilin Zhang,&nbsp;Jianfu Chen,&nbsp;Shenglin Zhou","doi":"10.1002/jcd.21924","DOIUrl":"10.1002/jcd.21924","url":null,"abstract":"<p>Let <math>\u0000 \u0000 <mrow>\u0000 <mi>D</mi>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>P</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>ℬ</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow></math> be a nontrivial symmetric <math>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>v</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>k</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>λ</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow></math>-design with <math>\u0000 \u0000 <mrow>\u0000 <mi>λ</mi>\u0000 \u0000 <mo>≤</mo>\u0000 \u0000 <mn>100</mn>\u0000 </mrow></math>, and let <math>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow></math> be a flag-transitive automorphism group of <math>\u0000 \u0000 <mrow>\u0000 <mi>D</mi>\u0000 </mrow></math>. In this paper, we show that if <math>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow></math> is quasiprimitive on <math>\u0000 \u0000 <mrow>\u0000 <mi>P</mi>\u0000 </mrow></math>, then <math>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow></math> is of holomorph affine or almost simple type. Moreover, if <math>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow></math> is imprimitive on <math>\u0000 \u0000 <mrow>\u0000 <mi>P</mi>\u0000 </mrow></math>, then <math>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow></math> is of almost simple type. According to this observation and to the classification of the finite simple groups we determine all such symmetric designs and the corresponding automorphism groups. We conclude with two open problems and a conjecture.</p>","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"32 3","pages":"107-126"},"PeriodicalIF":0.7,"publicationDate":"2023-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135726222","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}

{"title":"Dual incidences and t-designs in vector spaces","authors":"Kristijan Tabak","doi":"10.1002/jcd.21922","DOIUrl":"https://doi.org/10.1002/jcd.21922","url":null,"abstract":"&lt;p&gt;Let &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;V&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; $V$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be an &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; $n$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-dimensional vector space over &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 \u0000 &lt;mi&gt;q&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; ${{mathbb{F}}}_{q}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; ${rm{ {mathcal H} }}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is any set of &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; $k$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-dimensional subspaces of &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;V&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; $V$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. We construct two incidence structures &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;m&lt;/mi&gt;\u0000 \u0000 &lt;mi&gt;a&lt;/mi&gt;\u0000 \u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 \u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; ${{mathscr{D}}}_{max}({rm{ {mathcal H} }})$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;m&lt;/mi&gt;\u0000 \u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 \u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 \u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; ${{mathscr{D}}}_{min}({rm{ {mathcal H} }})$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; using subspaces from &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; ${rm{ {mathcal H} }}$&lt;/annotation&gt;\u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"32 1","pages":"46-52"},"PeriodicalIF":0.7,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134805714","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}