Extending the -design concept

Authors:
A. R. Calderbank and P. Delsarte

Journal:
Trans. Amer. Math. Soc. **338** (1993), 941-952

MSC:
Primary 05E30; Secondary 05B05, 33C45

MathSciNet review:
1134756

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a family of -subsets of a -set , with . Given only the inner distribution of , i.e., the number of pairs of blocks that meet in points (with ), we are able to completely describe the regularity with which meets an arbitrary -subset of , for each order (with ). This description makes use of a linear transform based on a system of dual Hahn polynomials with parameters , , . The main regularity parameter is the dimension of a well-defined subspace of , called the -form space of . (This subspace coincides with if and only if is a -design.) We show that the -form space has the structure of an ideal, and we explain how to compute its canonical generator.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1993-1134756-0

Keywords:
-design,
-form space,
-distribution matrix,
dual Hahn polynomials

Article copyright:
© Copyright 1993
American Mathematical Society