The p-ranks of residual and derived skew Hadamard designs

Hacioglu I., Michael T. S.

DISCRETE MATHEMATICS, vol.311, no.20, pp.2216-2219, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 311 Issue: 20
  • Publication Date: 2011
  • Doi Number: 10.1016/j.disc.2011.07.009
  • Journal Name: DISCRETE MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2216-2219
  • Çanakkale Onsekiz Mart University Affiliated: Yes

Abstract

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.