Disjoint maximal arcs in projective planes of order 16

Mustafa Gezek

Makale detayları

Disjoint maximal arcs in projective planes of order 16

Yazarlar:

Mustafa Gezek

Yayıncı:

Yildiz Technical University

Ana Başlıklar:

Biochemistry and Cell Biology (Other)

Dergi:

Sigma Journal of Engineering and Natural Sciences Vol.42 Issue 1, pp.82-88

Belge Tipi:

Makale

Yayın Tarihi:

2/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001312362

pISSN:

1304-7191

Anahtar kelimeler:

Özet:

 This paper provides the results of some computer searches for disjoint maximal 52, 4-arcs in the known planes of order 16. Thirty-seven new such sets are discovered: four in Johnson plane and thirty-three in Mathon plane, eighteen of which give examples of 104-sets of type 4,8 coming from non-isomorphic pairs of maximal 52, 4-arcs, providing first examples for such sets. A new lower bound on the number of 104-sets of type 4,8 coming from disjoint maximal 52, 4-arcs in the known planes of order 16 is obtained. The 104-length binary and ternary linear codes generated by the blocks of 1-designs associated with the known 104-sets of type 4,8 are classified.

 This paper provides the results of some computer searches for disjoint maximal 52, 4-arcs in the known planes of order 16. Thirty-seven new such sets are discovered: four in Johnson plane and thirty-three in Mathon plane, eighteen of which give examples of 104-sets of type 4,8 coming from non-isomorphic pairs of maximal 52, 4-arcs, providing first examples for such sets. A new lower bound on the number of 104-sets of type 4,8 coming from disjoint maximal 52, 4-arcs in the known planes of order 16 is obtained. The 104-length binary and ternary linear codes generated by the blocks of 1-designs associated with the known 104-sets of type 4,8 are classified.

 This paper provides the results of some computer searches for disjoint maximal 52, 4-arcs in the known planes of order 16. Thirty-seven new such sets are discovered: four in Johnson plane and thirty-three in Mathon plane, eighteen of which give examples of 104-sets of type 4,8 coming from non-isomorphic pairs of maximal 52, 4-arcs, providing first examples for such sets. A new lower bound on the number of 104-sets of type 4,8 coming from disjoint maximal 52, 4-arcs in the known planes of order 16 is obtained. The 104-length binary and ternary linear codes generated by the blocks of 1-designs associated with the known 104-sets of type 4,8 are classified.

 This paper provides the results of some computer searches for disjoint maximal 52, 4-arcs in the known planes of order 16. Thirty-seven new such sets are discovered: four in Johnson plane and thirty-three in Mathon plane, eighteen of which give examples of 104-sets of type 4,8 coming from non-isomorphic pairs of maximal 52, 4-arcs, providing first examples for such sets. A new lower bound on the number of 104-sets of type 4,8 coming from disjoint maximal 52, 4-arcs in the known planes of order 16 is obtained. The 104-length binary and ternary linear codes generated by the blocks of 1-designs associated with the known 104-sets of type 4,8 are classified.

Makale detayları

Disjoint maximal arcs in projective planes of order 16

Yazarlar:

Mustafa Gezek

Yayıncı:

Yildiz Technical University

Ana Başlıklar:

Biochemistry and Cell Biology (Other)

Dergi:

Sigma Journal of Engineering and Natural Sciences Vol.42 Issue 1, pp.82-88

Belge Tipi:

Makale

Yayın Tarihi:

2/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001312362

pISSN:

1304-7191

Disjoint Maximal ARC

Linear Code

Projective Plane

Sayı

Makale detayları

Disjoint maximal arcs in projective planes of order 16

Yazarlar: Mustafa Gezek

Yayıncı: Yildiz Technical University

Ana Başlıklar: Biochemistry and Cell Biology (Other)

Dergi: Sigma Journal of Engineering and Natural Sciences Vol.42 Issue 1, pp.82-88

Belge Tipi: Makale

Yayın Tarihi: 2/2024

Belge Dili: İngilizce

Document ID (Org No.): 2001312362

pISSN: 1304-7191

Disjoint Maximal ARC

Linear Code

Projective Plane

Sayı

Yazarlar:

Mustafa Gezek

Yayıncı:

Yildiz Technical University

Ana Başlıklar:

Biochemistry and Cell Biology (Other)

Dergi:

Sigma Journal of Engineering and Natural Sciences Vol.42 Issue 1, pp.82-88

Belge Tipi:

Makale

Yayın Tarihi:

2/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001312362

pISSN:

1304-7191