Classification and Construction of (k,3)-Arcs on Projective Plane Over Galois Field GF(9)
In this work, we construct and classify the projectively distinct (k,3)-arcs in PG(2,9), where k ≥ 5, and prove that the complete (k,3)-arcs do not exist, where 5 ≤ k ≤ 13. We found that the maximum complete (k,3)-arc in PG(2,q) is the (16,3)-arc and the minimum complete (k,3)-arc in PG(2,q...
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| Format: | Article |
| Language: | English |
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University of Baghdad
2017-04-01
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| Series: | Ibn Al-Haitham Journal for Pure and Applied Sciences |
| Subjects: | |
| Online Access: | https://jih.uobaghdad.edu.iq/index.php/j/article/view/533 |
| _version_ | 1811309374035984384 |
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| author | Adil M. Ahmad Amaal SH. Al-Mukhtar Fatima. F. Kareem |
| author_facet | Adil M. Ahmad Amaal SH. Al-Mukhtar Fatima. F. Kareem |
| author_sort | Adil M. Ahmad |
| collection | DOAJ |
| description |
In this work, we construct and classify the projectively distinct (k,3)-arcs in PG(2,9), where k ≥ 5, and prove that the complete (k,3)-arcs do not exist, where 5 ≤ k ≤ 13. We found that the maximum complete (k,3)-arc in PG(2,q) is the (16,3)-arc and the minimum complete (k,3)-arc in PG(2,q) is the (14,3)-arc. Moreover, we found the complete (k,3)-arcs between them.
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| first_indexed | 2024-04-13T09:41:04Z |
| format | Article |
| id | doaj.art-9075e24bed2b48c0bfaffc63986ef403 |
| institution | Directory Open Access Journal |
| issn | 1609-4042 2521-3407 |
| language | English |
| last_indexed | 2024-04-13T09:41:04Z |
| publishDate | 2017-04-01 |
| publisher | University of Baghdad |
| record_format | Article |
| series | Ibn Al-Haitham Journal for Pure and Applied Sciences |
| spelling | doaj.art-9075e24bed2b48c0bfaffc63986ef4032022-12-22T02:51:55ZengUniversity of BaghdadIbn Al-Haitham Journal for Pure and Applied Sciences1609-40422521-34072017-04-01261Classification and Construction of (k,3)-Arcs on Projective Plane Over Galois Field GF(9)Adil M. AhmadAmaal SH. Al-MukhtarFatima. F. Kareem In this work, we construct and classify the projectively distinct (k,3)-arcs in PG(2,9), where k ≥ 5, and prove that the complete (k,3)-arcs do not exist, where 5 ≤ k ≤ 13. We found that the maximum complete (k,3)-arc in PG(2,q) is the (16,3)-arc and the minimum complete (k,3)-arc in PG(2,q) is the (14,3)-arc. Moreover, we found the complete (k,3)-arcs between them. https://jih.uobaghdad.edu.iq/index.php/j/article/view/533arcs, secant, Projective plane ,Galois Field |
| spellingShingle | Adil M. Ahmad Amaal SH. Al-Mukhtar Fatima. F. Kareem Classification and Construction of (k,3)-Arcs on Projective Plane Over Galois Field GF(9) Ibn Al-Haitham Journal for Pure and Applied Sciences arcs, secant, Projective plane ,Galois Field |
| title | Classification and Construction of (k,3)-Arcs on Projective Plane Over Galois Field GF(9) |
| title_full | Classification and Construction of (k,3)-Arcs on Projective Plane Over Galois Field GF(9) |
| title_fullStr | Classification and Construction of (k,3)-Arcs on Projective Plane Over Galois Field GF(9) |
| title_full_unstemmed | Classification and Construction of (k,3)-Arcs on Projective Plane Over Galois Field GF(9) |
| title_short | Classification and Construction of (k,3)-Arcs on Projective Plane Over Galois Field GF(9) |
| title_sort | classification and construction of k 3 arcs on projective plane over galois field gf 9 |
| topic | arcs, secant, Projective plane ,Galois Field |
| url | https://jih.uobaghdad.edu.iq/index.php/j/article/view/533 |
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