Binary (<i>k</i>, <i>k</i>)-Designs
We introduce and investigate binary <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>k</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></semantics></math></inline-formula&...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/11/1883 |
| _version_ | 1827703181601144832 |
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| author | Todorka Alexandrova Peter Boyvalenkov Angel Dimitrov |
| author_facet | Todorka Alexandrova Peter Boyvalenkov Angel Dimitrov |
| author_sort | Todorka Alexandrova |
| collection | DOAJ |
| description | We introduce and investigate binary <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>k</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></semantics></math></inline-formula>-designs, a special case of <i>T</i>-designs. Our combinatorial interpretation relates <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>k</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></semantics></math></inline-formula>-designs to the binary orthogonal arrays. We derive a general linear programming bound and propose as a consequence a universal bound on the minimum possible cardinality of <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>k</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></semantics></math></inline-formula>-designs for fixed <i>k</i> and <i>n</i>. Designs which attain our bound are investigated. |
| first_indexed | 2024-03-10T15:12:47Z |
| format | Article |
| id | doaj.art-35eed5979b0d4ecaab964569c3809fcc |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T15:12:47Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-35eed5979b0d4ecaab964569c3809fcc2023-11-20T19:09:45ZengMDPI AGMathematics2227-73902020-10-01811188310.3390/math8111883Binary (<i>k</i>, <i>k</i>)-DesignsTodorka Alexandrova0Peter Boyvalenkov1Angel Dimitrov2Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 G Bonchev Str., 1113 Sofia, BulgariaInstitute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 G Bonchev Str., 1113 Sofia, BulgariaDepartment of Mathematics, Technical University Munich, Boltzmannstrasse 3, Garching b. 85748 Munich, GermanyWe introduce and investigate binary <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>k</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></semantics></math></inline-formula>-designs, a special case of <i>T</i>-designs. Our combinatorial interpretation relates <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>k</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></semantics></math></inline-formula>-designs to the binary orthogonal arrays. We derive a general linear programming bound and propose as a consequence a universal bound on the minimum possible cardinality of <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>k</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></semantics></math></inline-formula>-designs for fixed <i>k</i> and <i>n</i>. Designs which attain our bound are investigated.https://www.mdpi.com/2227-7390/8/11/1883binary (<i>k</i>,<i>k</i>)-designsorthogonal arrayslinear programming |
| spellingShingle | Todorka Alexandrova Peter Boyvalenkov Angel Dimitrov Binary (<i>k</i>, <i>k</i>)-Designs Mathematics binary (<i>k</i>,<i>k</i>)-designs orthogonal arrays linear programming |
| title | Binary (<i>k</i>, <i>k</i>)-Designs |
| title_full | Binary (<i>k</i>, <i>k</i>)-Designs |
| title_fullStr | Binary (<i>k</i>, <i>k</i>)-Designs |
| title_full_unstemmed | Binary (<i>k</i>, <i>k</i>)-Designs |
| title_short | Binary (<i>k</i>, <i>k</i>)-Designs |
| title_sort | binary i k i i k i designs |
| topic | binary (<i>k</i>,<i>k</i>)-designs orthogonal arrays linear programming |
| url | https://www.mdpi.com/2227-7390/8/11/1883 |
| work_keys_str_mv | AT todorkaalexandrova binaryikiikidesigns AT peterboyvalenkov binaryikiikidesigns AT angeldimitrov binaryikiikidesigns |