Journal of Combinatorial Designs最新文献

Putatively Optimal Projective Spherical Designs With Little Apparent Symmetry

IF 0.5 4区数学

Journal of Combinatorial Designs Pub Date : 2025-03-11 DOI: 10.1002/jcd.21979

Alex Elzenaar, Shayne Waldron

{"title":"Putatively Optimal Projective Spherical Designs With Little Apparent Symmetry","authors":"Alex Elzenaar, Shayne Waldron","doi":"10.1002/jcd.21979","DOIUrl":"https://doi.org/10.1002/jcd.21979","url":null,"abstract":"We give some new explicit examples of putatively optimal projective spherical designs, that is, ones for which there is numerical evidence that they are of minimal size. These form continuous families, and so have little apparent symmetry in general, which requires the introduction of new techniques for their construction. New examples of interest include an 11-point spherical <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mn>3</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>3</mn>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-design for <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msup>\u0000 <mi>R</mi>\u0000 \u0000 <mn>3</mn>\u0000 </msup>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, and a 12-point spherical <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mn>2</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-design for <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msup>\u0000 <mi>R</mi>\u0000 \u0000 <mn>4</mn>\u0000 </msup>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> given by four Mercedes-Benz frames that lie on equi-isoclinic planes. The latter example shows that the set of optimal spherical designs can be uncountable. We also give results of an extensive numerical study to determine the nature of the real algebraic variety of optimal projective real spherical designs, and in particular when it is a single point (a unique design) or corresponds to an infinite family of designs.","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"33 6","pages":"222-234"},"PeriodicalIF":0.5,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jcd.21979","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143845833","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

A Classification of the Flag-Transitive 2- ( v , 3 , λ ) Designs With v ≡ 1 , 3 ( mod 6 ) and v ≡ 6 ( mod λ )

IF 0.5 4区数学

Journal of Combinatorial Designs Pub Date : 2025-03-05 DOI: 10.1002/jcd.21978

Alessandro Montinaro, Eliana Francot

{"title":"A Classification of the Flag-Transitive 2-\u0000 \u0000 \u0000 \u0000 \u0000 (\u0000 \u0000 v\u0000 ,\u0000 3\u0000 ,\u0000 λ\u0000 \u0000 )\u0000 \u0000 \u0000 \u0000 Designs With \u0000 \u0000 \u0000 \u0000 v\u0000 ≡\u0000 1\u0000 ,\u0000 3\u0000 \u0000 \u0000 (\u0000 \u0000 mod\u0000 \u0000 6\u0000 \u0000 )\u0000 \u0000 \u0000 \u0000 and \u0000 \u0000 \u0000 \u0000 v\u0000 ≡\u0000 6\u0000 \u0000 \u0000 (\u0000 \u0000 mod\u0000 \u0000 λ\u0000 \u0000 )","authors":"Alessandro Montinaro, Eliana Francot","doi":"10.1002/jcd.21978","DOIUrl":"https://doi.org/10.1002/jcd.21978","url":null,"abstract":"<div>\u0000 \u0000 In this paper, we provide a complete classification of the 2-<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>3</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>λ</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> designs with <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>v</mi>\u0000 \u0000 <mo>≡</mo>\u0000 \u0000 <mn>1</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>3</mn>\u0000 <mspace></mspace>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>mod</mi>\u0000 <mspace></mspace>\u0000 \u0000 <mn>6</mn>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>v</mi>\u0000 \u0000 <mo>≡</mo>\u0000 \u0000 <mn>6</mn>\u0000 <mspace></mspace>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>mod</mi>\u0000 <mspace></mspace>\u0000 \u0000 <mi>λ</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> admitting a flag-transitive automorphism group non-isomorphic to a subgroup of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>A</mi>\u0000 \u0000 <mi>Γ</mi>\u0000 \u0000 <msub>\u0000 <mi>L</mi>\u0000 \u0000 <mn>1</mn>\u0000 </msub>\u0000 \u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"33 6","pages":"217-221"},"PeriodicalIF":0.5,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143846041","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

GDD Type Spanning Bipartite Block Designs

IF 0.5 4区数学

Journal of Combinatorial Designs Pub Date : 2025-02-27 DOI: 10.1002/jcd.21976

Shoko Chisaki, Ryoh Fuji-Hara, Nobuko Miyamoto

{"title":"GDD Type Spanning Bipartite Block Designs","authors":"Shoko Chisaki, Ryoh Fuji-Hara, Nobuko Miyamoto","doi":"10.1002/jcd.21976","DOIUrl":"https://doi.org/10.1002/jcd.21976","url":null,"abstract":"<div>\u0000 \u0000 There is a one-to-one correspondence between the point set of a group divisible design (GDD) with <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>v</mi>\u0000 \u0000 <mn>1</mn>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> groups of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>v</mi>\u0000 \u0000 <mn>2</mn>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> points and the edge set of a complete bipartite graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>K</mi>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>v</mi>\u0000 \u0000 <mn>1</mn>\u0000 </msub>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msub>\u0000 <mi>v</mi>\u0000 \u0000 <mn>2</mn>\u0000 </msub>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. A block of GDD corresponds to a subgraph of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>K</mi>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>v</mi>\u0000 \u0000 <mn>1</mn>\u0000 </msub>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msub>\u0000 <mi>v</mi>\u0000 \u0000 <mn>2</mn>\u0000 </msub>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. We show that the concurrence conditions of two points of GDD can correspond to the edge concurrence conditions of subgraphs of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>K</mi>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"33 6","pages":"207-216"},"PeriodicalIF":0.5,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143845859","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

Cycle Switching in Steiner Triple Systems of Order 19

IF 0.5 4区数学

Journal of Combinatorial Designs Pub Date : 2025-02-27 DOI: 10.1002/jcd.21975

Grahame Erskine, Terry S. Griggs

{"title":"Cycle Switching in Steiner Triple Systems of Order 19","authors":"Grahame Erskine, Terry S. Griggs","doi":"10.1002/jcd.21975","DOIUrl":"https://doi.org/10.1002/jcd.21975","url":null,"abstract":"<div>\u0000 \u0000 Cycle switching is a particular form of transformation applied to isomorphism classes of a Steiner triple system of a given order <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>v</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> (an <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mtext>STS</mtext>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>v</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>), yielding another <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mtext>STS</mtext>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>v</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. This relationship may be represented by an undirected graph. An <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mtext>STS</mtext>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>v</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> admits cycles of lengths <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mn>4</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>6</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>…</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>v</mi>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mn>7</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>v</mi>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mn>3</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. In the particular case of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"33 5","pages":"195-204"},"PeriodicalIF":0.5,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595458","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

More Heffter Spaces via Finite Fields

IF 0.5 4区数学

Journal of Combinatorial Designs Pub Date : 2025-02-23 DOI: 10.1002/jcd.21974

Marco Buratti, Anita Pasotti

{"title":"More Heffter Spaces via Finite Fields","authors":"Marco Buratti, Anita Pasotti","doi":"10.1002/jcd.21974","DOIUrl":"https://doi.org/10.1002/jcd.21974","url":null,"abstract":"<div>\u0000 \u0000 A <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 <mi>k</mi>\u0000 \u0000 <mo>;</mo>\u0000 \u0000 <mi>r</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> Heffter space is a resolvable <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>v</mi>\u0000 \u0000 <mi>r</mi>\u0000 </msub>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msub>\u0000 <mi>b</mi>\u0000 \u0000 <mi>k</mi>\u0000 </msub>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> configuration whose points form a half-set of an abelian group <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and whose blocks are all zero-sum in <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. It was recently proved that there are infinitely many orders <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>v</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> for which, given any pair <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>r</mi>\u0000 </mrow>\u0000 \u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"33 5","pages":"188-194"},"PeriodicalIF":0.5,"publicationDate":"2025-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595699","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

Pairs in Nested Steiner Quadruple Systems

IF 0.5 4区数学

Journal of Combinatorial Designs Pub Date : 2025-02-20 DOI: 10.1002/jcd.21973

Yeow Meng Chee, Son Hoang Dau, Tuvi Etzion, Han Mao Kiah, Wenqin Zhang

{"title":"Pairs in Nested Steiner Quadruple Systems","authors":"Yeow Meng Chee, Son Hoang Dau, Tuvi Etzion, Han Mao Kiah, Wenqin Zhang","doi":"10.1002/jcd.21973","DOIUrl":"https://doi.org/10.1002/jcd.21973","url":null,"abstract":"<div>\u0000 \u0000 Motivated by a repair problem for fractional repetition codes in distributed storage, each block of any Steiner quadruple system (SQS) of order <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>v</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is partitioned into two pairs. Each pair in such a partition is called a nested design pair, and its multiplicity is the number of times it is a pair in this partition. Such a partition of each block is considered a new block design called a nested SQS. Several related questions on this type of design are considered in this paper: What is the maximum multiplicity of the nested design pair with minimum multiplicity? What is the minimum multiplicity of the nested design pair with maximum multiplicity? Are there nested quadruple systems in which all the nested design pairs have the same multiplicity? Of special interest are nested quadruple systems in which all the <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mfenced>\u0000 <mfrac>\u0000 <mi>v</mi>\u0000 \u0000 <mn>2</mn>\u0000 </mfrac>\u0000 </mfenced>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> pairs are nested design pairs with the same multiplicity. Several constructions of nested quadruple systems are considered, and in particular, classic constructions of SQS are examined.\u0000 </div>","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"33 5","pages":"177-187"},"PeriodicalIF":0.5,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595452","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 Families of Strength-3 Covering Arrays Using Linear Feedback Shift Register Sequences

IF 0.5 4区数学

Journal of Combinatorial Designs Pub Date : 2025-02-14 DOI: 10.1002/jcd.21963

Kianoosh Shokri, Lucia Moura

{"title":"New Families of Strength-3 Covering Arrays Using Linear Feedback Shift Register Sequences","authors":"Kianoosh Shokri, Lucia Moura","doi":"10.1002/jcd.21963","DOIUrl":"https://doi.org/10.1002/jcd.21963","url":null,"abstract":"In an array over an alphabet of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mi>v</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> symbols, a <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-set of column indices <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>{</mo>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>c</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>c</mi>\u0000 \u0000 <mi>t</mi>\u0000 </msub>\u0000 </mrow>\u0000 \u0000 <mo>}</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is covered if each <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-tuple of the alphabet occurs at least once as a row of the sub-array indexed by <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <msub>\u0000 <mi>c</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>c</mi>\u0000 \u0000 <mi>t</mi>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. A covering array, denoted by CA<math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>N</mi>\u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"33 4","pages":"156-171"},"PeriodicalIF":0.5,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jcd.21963","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143446750","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

On MSRD Codes, h-Designs and Disjoint Maximum Scattered Linear Sets

IF 0.5 4区数学

Journal of Combinatorial Designs Pub Date : 2025-01-29 DOI: 10.1002/jcd.21972

Paolo Santonastaso, John Sheekey

{"title":"On MSRD Codes, h-Designs and Disjoint Maximum Scattered Linear Sets","authors":"Paolo Santonastaso, John Sheekey","doi":"10.1002/jcd.21972","DOIUrl":"https://doi.org/10.1002/jcd.21972","url":null,"abstract":"<div>\u0000 \u0000 In this paper, we construct new optimal subspace designs and, consequently, new optimal codes in the sum-rank metric. We construct new 1-designs by finding sets of disjoint maximum scattered linear sets, and use these constructions to also find new <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mi>h</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-designs for <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mi>h</mi>\u0000 <mo>></mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. As a means of achieving this, we establish a correspondence between the metric properties of sum-rank metric codes and the geometric properties of subspace designs. Specifically, we determine the geometric counterpart of the coding-theoretic notion of generalised weights for the sum-rank metric in terms of subspace designs and determine a geometric characterisation of MSRD codes. This enables us to characterise subspace designs via their intersections with hyperplanes and via duality operations.\u0000 </div>","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"33 4","pages":"137-155"},"PeriodicalIF":0.5,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143447152","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

Bent Functions on Finite Nonabelian Groups and Relative Difference Sets

IF 0.5 4区数学

Journal of Combinatorial Designs Pub Date : 2025-01-16 DOI: 10.1002/jcd.21970

Bangteng Xu

{"title":"Bent Functions on Finite Nonabelian Groups and Relative Difference Sets","authors":"Bangteng Xu","doi":"10.1002/jcd.21970","DOIUrl":"https://doi.org/10.1002/jcd.21970","url":null,"abstract":"<div>\u0000 \u0000 It is well known that the perfect nonlinearity of a function between finite groups <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> can be characterized by its graph in terms of relative difference set in the direct product <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 \u0000 <mo>×</mo>\u0000 \u0000 <mi>H</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> (cf. [4]). Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> be the infinite set of complex roots of unity. A <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-valued function <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> on an arbitrary finite group <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is associated with a finite cyclic subgroup <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <msub>\u0000 <mi>T</mi>\u0000 \u0000 <mi>f</mi>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> in the multiplicative group of nonzero complex numbers. For a bent function <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> on <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> in general, its graph is not a relative difference set in the direct product <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 \u0000 <mo>×</mo>\u0000 \u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"33 4","pages":"125-136"},"PeriodicalIF":0.5,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143446694","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

Extensions of Steiner Triple Systems

IF 0.5 4区数学

Journal of Combinatorial Designs Pub Date : 2025-01-06 DOI: 10.1002/jcd.21964

Giovanni Falcone, Agota Figula, Mario Galici

引用次数: 0