Journal of Combinatorial Designs最新文献_第5页

Group divisible designs with block size 4 and group sizes 4 and 7 组块大小为 4，组块大小为 4 和 7 的可分割设计

IF 0.7 4区数学

Journal of Combinatorial Designs Pub Date : 2024-03-28 DOI: 10.1002/jcd.21932

R. Julian R. Abel, Thomas Britz, Yudhistira A. Bunjamin, Diana Combe

{"title":"Group divisible designs with block size 4 and group sizes 4 and 7","authors":"R. Julian R. Abel, Thomas Britz, Yudhistira A. Bunjamin, Diana Combe","doi":"10.1002/jcd.21932","DOIUrl":"https://doi.org/10.1002/jcd.21932","url":null,"abstract":"In this paper, we consider the existence of group divisible designs (GDDs) with block size <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>4</mn>\u0000 </mrow>\u0000 <annotation> $4$</annotation>\u0000 </semantics></math> and group sizes <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>4</mn>\u0000 </mrow>\u0000 <annotation> $4$</annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>7</mn>\u0000 </mrow>\u0000 <annotation> $7$</annotation>\u0000 </semantics></math>. We show that there exists a <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>4</mn>\u0000 </mrow>\u0000 <annotation> $4$</annotation>\u0000 </semantics></math>-GDD of type <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mn>4</mn>\u0000 <mi>t</mi>\u0000 </msup>\u0000 <msup>\u0000 <mn>7</mn>\u0000 <mi>s</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation> ${4}^{t}{7}^{s}$</annotation>\u0000 </semantics></math> for all but a finite specified set of feasible values for <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 <mo>,</mo>\u0000 <mi>s</mi>\u0000 </mrow>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $(t,s)$</annotation>\u0000 </semantics></math>.","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"32 6","pages":"328-346"},"PeriodicalIF":0.7,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jcd.21932","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140553167","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

Alternating parity weak sequencing 交替奇偶校验弱排序

IF 0.7 4区数学

Journal of Combinatorial Designs Pub Date : 2024-02-27 DOI: 10.1002/jcd.21936

Simone Costa, Stefano Della Fiore

{"title":"Alternating parity weak sequencing","authors":"Simone Costa, Stefano Della Fiore","doi":"10.1002/jcd.21936","DOIUrl":"10.1002/jcd.21936","url":null,"abstract":"A subset <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 </mrow>\u0000 <annotation> $S$</annotation>\u0000 </semantics></math> of a group <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mo>+</mo>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation> $(G,+)$</annotation>\u0000 </semantics></math> is <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 <annotation> $t$</annotation>\u0000 </semantics></math>-weakly sequenceable if there is an ordering <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mrow>\u0000 <msub>\u0000 <mi>y</mi>\u0000 \u0000 <mn>1</mn>\u0000 </msub>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>…</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msub>\u0000 <mi>y</mi>\u0000 \u0000 <mi>k</mi>\u0000 </msub>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation> $({y}_{1},{rm{ldots }},{y}_{k})$</annotation>\u0000 </semantics></math> of its elements such that the partial sums <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>s</mi>\u0000 \u0000 <mn>0</mn>\u0000 </msub>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msub>\u0000 <mi>s</mi>\u0000 \u0000 <mn>1</mn>\u0000 </msub>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>…</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msub>\u0000 <mi>s</mi>\u0000 \u0000 <mi>k</mi>\u0000 </msub>\u0000 </mrow>\u0000 <annotation> ${s}_{0},{s}_{1},{rm{ldots }},{s}_{k}$</annotation>\u0000 </semantics></math>, given by <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>s</mi>\u0000 \u0000 <mn>0</mn>\u0000 </msub>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation> ${s}_{0}=0$</annotation>\u0000 </","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"32 6","pages":"308-327"},"PeriodicalIF":0.7,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139978158","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

The existence of 2 3 ${2}^{3}$ -decomposable super-simple ( v , 4 , 6 ) $(v,4,6)$ -BIBDs 存在23个可分解的超简单（v,4,6）$(v,4,6)$-BIBDs

IF 0.7 4区数学

Journal of Combinatorial Designs Pub Date : 2024-02-22 DOI: 10.1002/jcd.21935

Huangsheng Yu, Jingyuan Chen, R. Julian R. Abel, Dianhua Wu

{"title":"The existence of \u0000 \u0000 \u0000 \u0000 2\u0000 3\u0000 \u0000 \u0000 ${2}^{3}$\u0000 -decomposable super-simple \u0000 \u0000 \u0000 \u0000 (\u0000 \u0000 v\u0000 ,\u0000 4\u0000 ,\u0000 6\u0000 \u0000 )\u0000 \u0000 \u0000 $(v,4,6)$\u0000 -BIBDs","authors":"Huangsheng Yu, Jingyuan Chen, R. Julian R. Abel, Dianhua Wu","doi":"10.1002/jcd.21935","DOIUrl":"10.1002/jcd.21935","url":null,"abstract":"A design is said to be super-simple if the intersection of any two blocks has at most two elements. A design with index <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 <mi>λ</mi>\u0000 </mrow>\u0000 <annotation> $tlambda $</annotation>\u0000 </semantics></math> is said to be <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>λ</mi>\u0000 <mi>t</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation> ${lambda }^{t}$</annotation>\u0000 </semantics></math>-decomposable, if its blocks can be partitioned into nonempty collections <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>B</mi>\u0000 <mi>i</mi>\u0000 </msub>\u0000 </mrow>\u0000 <annotation> ${{rm{ {mathcal B} }}}_{i}$</annotation>\u0000 </semantics></math>, <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>≤</mo>\u0000 <mi>i</mi>\u0000 <mo>≤</mo>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 <annotation> $1le ile t$</annotation>\u0000 </semantics></math>, such that each <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>B</mi>\u0000 <mi>i</mi>\u0000 </msub>\u0000 </mrow>\u0000 <annotation> ${{rm{ {mathcal B} }}}_{i}$</annotation>\u0000 </semantics></math> with the point set forms a design with index <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 </mrow>\u0000 <annotation> $lambda $</annotation>\u0000 </semantics></math>. In this paper, it is proved that there exists a <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mn>2</mn>\u0000 <mn>3</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation> ${2}^{3}$</annotation>\u0000 </semantics></math>-decomposable super-simple <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mrow>\u0000 <mi>v</mi>\u0000 <mo>,</mo>\u0000 <mn>4</mn>\u0000 <mo>,</mo>\u0000 <mn>6</mn>\u0000 </mrow>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $(v,4,6)$</annotation>\u0000 </semantics></math>-BIBD (balanced incomplete block design) if and only if <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>v</mi>\u0000 <mo>≥</mo>\u0000","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"32 6","pages":"297-307"},"PeriodicalIF":0.7,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139946643","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

Partition of ordered triples into uniform holey ordered designs 将有序三元组划分为均匀有序的洞穴设计

IF 0.7 4区数学

Journal of Combinatorial Designs Pub Date : 2024-02-19 DOI: 10.1002/jcd.21933

Yuli Tan, Junling Zhou

{"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":"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}

引用次数: 0

Geometric dual and sum-rank minimal codes 几何对偶码与和秩最小码

IF 0.7 4区数学

Journal of Combinatorial Designs Pub Date : 2024-02-14 DOI: 10.1002/jcd.21934

Martino Borello, Ferdinando Zullo

引用次数: 0

Constructing MRD codes by switching 通过切换构建 MRD 代码

IF 0.7 4区数学

Journal of Combinatorial Designs Pub Date : 2024-02-08 DOI: 10.1002/jcd.21931

Minjia Shi, Denis S. Krotov, Ferruh Özbudak

{"title":"Constructing MRD codes by switching","authors":"Minjia Shi, Denis S. Krotov, Ferruh Özbudak","doi":"10.1002/jcd.21931","DOIUrl":"10.1002/jcd.21931","url":null,"abstract":"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.","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}

引用次数: 0

New constructions for disjoint partial difference families and external partial difference families 不相交部分差分族和外部部分差分族的新构造

IF 0.7 4区数学

Journal of Combinatorial Designs Pub Date : 2024-02-04 DOI: 10.1002/jcd.21930

Sophie Huczynska, Laura Johnson

引用次数: 0

Sailing league problems 帆船联赛问题

IF 0.7 4区数学

Journal of Combinatorial Designs Pub Date : 2024-01-22 DOI: 10.1002/jcd.21929

Robert Schüler, Achill Schürmann

引用次数: 0

Sporadic simple groups as flag-transitive automorphism groups of symmetric designs 作为对称设计的旗转自形群的零星简单群