On the existence of (400, 57, 8) non-abelian difference sets

Adegoke Solomon OSIFODUNRIN

doi:https://doi.org/10.3906/mat-1106-9

Makale detayları

On the existence of (400, 57, 8) non-abelian difference sets

Yazarlar:

Adegoke Solomon OSIFODUNRIN

Yayıncı:

TUBITAK

Ana Başlıklar:

Matematik

Dergi:

Turkish Journal of Mathematics 2013 Vol.37 Issue 3, pp.375-390

Belge Tipi:

Makale

Yayın Tarihi:

2/2013

Belge Dili:

İngilizce

Document ID (Org No.):

2000747588

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

DOI:

https://doi.org/10.3906/mat-1106-9

Anahtar kelimeler:

Özet:

 

Difference sets with parameters (\frac{qd + 1 - 1}{q - 1},  \frac{qd - 1}{q - 1}, \frac{qd - 1 - 1}{q - 1}), where q is a  prime power and d \geq 1, are known to exist in cyclic groups and are  called classical Singer difference sets.  We study a special case of  this family with q = 7 and d = 3 in search of more difference sets.  According to GAP, there are 220 groups of order 400 out of which 10  are abelian.  E. Kopilovich and other authors showed that the  remaining nine abelian groups of order 400 do not admit (400, 57, 8)  difference sets.  Also, Gao and Wei used the (400, 57, 8) Singer  difference set to construct four inequivalent difference sets in a  non-abelian group.  In this paper, we demonstrate using group  representation and factorization in cyclotomic rings that, out of the  remaining 209 non-abelian groups of order 400, only 15 could possibly  admit (400, 57, 8) difference sets.

 

Difference sets with parameters (\frac{qd + 1 - 1}{q - 1},  \frac{qd - 1}{q - 1}, \frac{qd - 1 - 1}{q - 1}), where q is a  prime power and d \geq 1, are known to exist in cyclic groups and are  called classical Singer difference sets.  We study a special case of  this family with q = 7 and d = 3 in search of more difference sets.  According to GAP, there are 220 groups of order 400 out of which 10  are abelian.  E. Kopilovich and other authors showed that the  remaining nine abelian groups of order 400 do not admit (400, 57, 8)  difference sets.  Also, Gao and Wei used the (400, 57, 8) Singer  difference set to construct four inequivalent difference sets in a  non-abelian group.  In this paper, we demonstrate using group  representation and factorization in cyclotomic rings that, out of the  remaining 209 non-abelian groups of order 400, only 15 could possibly  admit (400, 57, 8) difference sets.

Makale detayları

On the existence of (400, 57, 8) non-abelian difference sets

Yazarlar:

Adegoke Solomon OSIFODUNRIN

Yayıncı:

TUBITAK

Ana Başlıklar:

Matematik

Dergi:

Turkish Journal of Mathematics 2013 Vol.37 Issue 3, pp.375-390

Belge Tipi:

Makale

Yayın Tarihi:

2/2013

Belge Dili:

İngilizce

Document ID (Org No.):

2000747588

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

DOI:

https://doi.org/10.3906/mat-1106-9

Representation

idempotents

Singer difference sets

intersection numbers

Sayı

Makale detayları

On the existence of (400, 57, 8) non-abelian difference sets

Yazarlar: Adegoke Solomon OSIFODUNRIN

Yayıncı: TUBITAK

Ana Başlıklar: Matematik

Dergi: Turkish Journal of Mathematics 2013 Vol.37 Issue 3, pp.375-390

Belge Tipi: Makale

Yayın Tarihi: 2/2013

Belge Dili: İngilizce

Document ID (Org No.): 2000747588

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

DOI: https://doi.org/10.3906/mat-1106-9

Representation

idempotents

Singer difference sets

intersection numbers

Sayı

Yazarlar:

Adegoke Solomon OSIFODUNRIN

Yayıncı:

TUBITAK

Ana Başlıklar:

Matematik

Dergi:

Turkish Journal of Mathematics 2013 Vol.37 Issue 3, pp.375-390

Belge Tipi:

Makale

Yayın Tarihi:

2/2013

Belge Dili:

İngilizce

Document ID (Org No.):

2000747588

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

DOI:

https://doi.org/10.3906/mat-1106-9