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Zbl 0611.33013
Chihara, Laura
On the zeros of the Askey-Wilson polynomials, with applications to coding theory. (English)
[J] SIAM J. Math. Anal. 18, 191-207 (1987). ISSN 0036-1410; ISSN 1095-7154/e

In a symmetric association scheme that is (P and Q)-polynomial, the P and Q eigenmatrices are given by balanced ${}\sb 4\Phi\sb 3$ Askey-Wilson polynomials. In this paper, the parameters of the Askey-Wilson polynomial are classified so that its zeros are not contained in its spectrum. These results, together with theorems of Biggs and Delsarte, imply the nonexistence of perfect codes and tight designs in the classical association schemes of type $A\sb N$, $B\sb N$, $C\sb N$, $D\sb N$ and the affine matrix schemes.

MSC 2000:: *33C45 Orthogonal polynomials and functions of hypergeometric type

Keywords: Askey-Wilson polynomials; perfect codes; tight designs; association schemes

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