Construction of orthogonal starters and its consequences
A method is proposed for constructing a system of (v−1)/2 pairwise disjoint orthogonal starters of order v for v ≡ 6k+1 ≡ 7 (mod 12) ≡ p ≡ (n2+n+1)/t such that the number 3 is one of the primitive roots of the Galois field of prime order p (k is prime, k ≠ 2, and n and t are positive integers). The...
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| Date: | 1992 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian |
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Institute of Mathematics, NAS of Ukraine
1992
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7962 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512831656427520 |
|---|---|
| author | Nazarok , A. V. Назарок , А. В. |
| author_facet | Nazarok , A. V. Назарок , А. В. |
| author_sort | Nazarok , A. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2023-12-01T10:43:23Z |
| description | A method is proposed for constructing a system of (v−1)/2 pairwise disjoint orthogonal starters of order v for v ≡ 6k+1 ≡ 7 (mod 12) ≡ p ≡ (n2+n+1)/t such that the number 3 is one of the primitive roots of the Galois field of prime order p (k is prime, k ≠ 2, and n and t are positive integers). The starters occurring in this system satisfy certain additional conditions. The construction of a series of combinatorial structures, including some not previously known, is a consequence of this result. |
| first_indexed | 2026-03-24T03:35:02Z |
| format | Article |
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| id | umjimathkievua-article-7962 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus |
| last_indexed | 2026-03-24T03:35:02Z |
| publishDate | 1992 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/d1/2bff7216b9605ff4d30741db43ab60d1.pdf |
| spelling | umjimathkievua-article-79622023-12-01T10:43:23Z Construction of orthogonal starters and its consequences Построение ортогональных стартеров и его следствия Nazarok , A. V. Назарок , А. В. A method is proposed for constructing a system of (v−1)/2 pairwise disjoint orthogonal starters of order v for v ≡ 6k+1 ≡ 7 (mod 12) ≡ p ≡ (n2+n+1)/t such that the number 3 is one of the primitive roots of the Galois field of prime order p (k is prime, k ≠ 2, and n and t are positive integers). The starters occurring in this system satisfy certain additional conditions. The construction of a series of combinatorial structures, including some not previously known, is a consequence of this result. Предложен метод построения системы (v-1)/2 попарно ортогональных стартеров порядка v для v ≡ 6k+1 ≡ 7 (mod 12) ≡ p ≡ (n2+n+1)/t таких, что одним из первообразных корней поля Галуа простого порядка р является число 3 (k — простое, k ≠ 2, n и t — целые положительные числа). При этом стартеры, входящие в данную систему, удовлетворяют некоторым дополнительным условиям. Следствием этого результата явилось построение ряда комбинаторных конструкций, в том числе ранее неизвестных. Запропоновано метод побудови системи (v-1)/2 попарно ортогональних стартерів порядку v для v ≡ 6k+1 ≡ 7 (mod 12) ≡ p ≡ (n2+n+1)/t таких, що одним із первісних коренів поля Галуа простого порядку р є число 3 (k — просте, k ≠ 2, n і t — цілі додатні числа). При ньому стартери, що входять в дану систему, задовольняють деякі додаткові умови. Наслідком цього результату є побудова ряду комбінаторних конструкцій, в тому числі раніше невідомих. Institute of Mathematics, NAS of Ukraine 1992-05-26 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/7962 Ukrains’kyi Matematychnyi Zhurnal; Vol. 44 No. 5 (1992); 654-662 Український математичний журнал; Том 44 № 5 (1992); 654-662 1027-3190 rus https://umj.imath.kiev.ua/index.php/umj/article/view/7962/9555 |
| spellingShingle | Nazarok , A. V. Назарок , А. В. Construction of orthogonal starters and its consequences |
| title | Construction of orthogonal starters and its consequences |
| title_alt | Построение ортогональных стартеров и его следствия |
| title_full | Construction of orthogonal starters and its consequences |
| title_fullStr | Construction of orthogonal starters and its consequences |
| title_full_unstemmed | Construction of orthogonal starters and its consequences |
| title_short | Construction of orthogonal starters and its consequences |
| title_sort | construction of orthogonal starters and its consequences |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7962 |
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