Shrikhande, M. S. ; Singhi, N. M.
(1990)
*An elementary derivation of the annihilator polynomial for extremal (2s+1)-designs*
Discrete Mathematics, 80
(1).
pp. 93-96.
ISSN 0012-365X

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Official URL: http://www.sciencedirect.com/science/article/pii/0...

Related URL: http://dx.doi.org/10.1016/0012-365X(90)90298-V

## Abstract

Let D be a (2s+1)-design with parameters (v, k, λ_{2s+1}). It is known that D has at least s+1 block intersection numbers x_{1}, x_{2}, ..., x_{s+1}. Suppose now D is an extremal (2s+1)-design with exactly s+1 intersection numbers. In this case we give a short proof of the following known result of Delsarte: The s+1 intersection numbers are roots of a polynomial whose coefficients depend only on the design parameters. Delsarte's result, proved more generally, for designs in Q-polynomial association schemes, uses the notion of the annihilator polynomial. Our proof relies on elementary ideas and part of an algorithm used for decoding BCH codes.

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ID Code: | 50442 |

Deposited On: | 23 Jul 2011 12:05 |

Last Modified: | 23 Jul 2011 12:05 |

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