An elementary derivation of the annihilator polynomial for extremal \((2s+1)\)-designs (Q912851)

A \((2s+1)\)-design is known to have at least \(s+1\) block intersection numbers; such a design is extremal when it has exactly \(s+1\). This paper gives an elementary proof of a theorem of Delsarte: the \(s+1\) block intersection numbers of an extremal \((2s+1)\)-design are roots of a polynomial whose coefficients depend only on the design parameters (t- (v,k,\(\lambda)\)). The proof is remarkably concise, and uses a portion of a standard method for decoding BCH codes.