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Extending the t-design concept

Publication ,  Journal Article
Calderbank, AR; Delsarte, P
Published in: Transactions of the American Mathematical Society
January 1, 1993

Let 픅 be a family of k-subsets of a υ-set V, with 1 ≤ k ≤ υ/2. Given only the inner distribution of 픅, i.e., the number of pairs of blocks that meet in j points (with j = 0, 1, …, k), we are able to completely describe the regularity with which 픅 meets an arbitrary t-subset of V, for each order t (with 1 ≤ t ≤ υ/2). This description makes use of a linear transform based on a system of dual Hahn polynomials with parameters υ, k, t. The main regularity parameter is the dimension of a well-defined subspace of ℝt+1, called the t-form space of 픅. (This subspace coincides with ℝt+1 if and only if 픅 is a t-design.) We show that the t-form space has the structure of an ideal, and we explain how to compute its canonical generator. © 1993 American Mathematical Society.

Duke Scholars

Published In

Transactions of the American Mathematical Society

DOI

ISSN

0002-9947

Publication Date

January 1, 1993

Volume

338

Issue

2

Start / End Page

941 / 952

Related Subject Headings

  • General Mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics
 

Citation

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Calderbank, A. R., & Delsarte, P. (1993). Extending the t-design concept. Transactions of the American Mathematical Society, 338(2), 941–952. https://doi.org/10.1090/S0002-9947-1993-1134756-0
Calderbank, A. R., and P. Delsarte. “Extending the t-design concept.” Transactions of the American Mathematical Society 338, no. 2 (January 1, 1993): 941–52. https://doi.org/10.1090/S0002-9947-1993-1134756-0.
Calderbank AR, Delsarte P. Extending the t-design concept. Transactions of the American Mathematical Society. 1993 Jan 1;338(2):941–52.
Calderbank, A. R., and P. Delsarte. “Extending the t-design concept.” Transactions of the American Mathematical Society, vol. 338, no. 2, Jan. 1993, pp. 941–52. Scopus, doi:10.1090/S0002-9947-1993-1134756-0.
Calderbank AR, Delsarte P. Extending the t-design concept. Transactions of the American Mathematical Society. 1993 Jan 1;338(2):941–952.
Journal cover image

Published In

Transactions of the American Mathematical Society

DOI

ISSN

0002-9947

Publication Date

January 1, 1993

Volume

338

Issue

2

Start / End Page

941 / 952

Related Subject Headings

  • General Mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics