The p-ranks of residual and derived skew Hadamard designs

Hacioglu I., Michael T. S.

DISCRETE MATHEMATICS, cilt.311, sa.20, ss.2216-2219, 2011 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 311 Sayı: 20
  • Basım Tarihi: 2011
  • Doi Numarası: 10.1016/j.disc.2011.07.009
  • Dergi Adı: DISCRETE MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2216-2219
  • Çanakkale Onsekiz Mart Üniversitesi Adresli: Evet

Özet

Let H be a Hadamard (4n - 1, 2n - 1, n - 1)-design. Suppose that the prime p divides n, but that p(2) does not divide n. A result of Klemm implies that every residual design of H has p-rank at least n. Also, every derived design of H has p-rank at least n if p not equal 2. We show that when H is a skew Hadamard design, the p-ranks of the residual and derived designs are at least n even if p(2) divides n or p = 2. We construct infinitely many examples where the p-rank is exactly n. Published by Elsevier B.V.